Going to be a bit of a wall (such a glorious wall that I'm scared the FBI is going to raid my house and throw me in jail), so I will add a TL

R at the end with some key points for those who don't want/need to understand the physics and mathematics behind our hobby.
Ok, so I've done a LOT of research into BB weight and ballistics due to my interest in long distance shooting in airsoft. Also, please bear in mind that this is, at the end of the day, a layman's explanation of this. I'm operating on A-level mathematics and GCSE physics here, and I haven't done them in about a decade. It's also really hard to explain this without a whiteboard or sheet of paper to draw diagrams and stuff, so bear with me I'll do my best to keep it accessible!
So, the maths behind our hobby! Kinetic energy is calculated by 1/2 x mass x (velocity x velocity), using brackets as order of operations means we do the squaring before the multiplication but it's easier to show this way exactly what I'm doing. However we can't just translate that to airsoft measurements of fractions of a gram and feet per second, as joules are calculated using mass in kg so really really small numbers in our context and velocity in metres per second, not feet per second. So a 0.2g BB shot at 328fps, which is 100m/s would calculate as:
Energy = 1/2 x 0.0002 x (100 x 100)
Energy = 0.0001 x 10000
Energy = 1J
Only reason I used 328fps instead of 350fps is to avoid plaguing you with weird numbers and make the example easier to follow. Really, feet per second is annoying and we should be using metres per second since it's easier to work with in terms of energy calculations. It's why springs are m100, m120 etc, as they're designed in m/s rather than ft/s. What we can take away from this is that mass and velocity work in tandem to calculate joules (I know, I'm big smart for drawing such a conclusion). However we need to briefly consider momentum to understand ballistics; my physics teacher always described momentum as "how much something will hurt when it hits you" and is a lot simpler than kinetic energy. Momentum = mass x velocity. Easy. I'm not going to bore you with the calculations I'm doing for this example now, but I'm looking at 1.14J on a .2 and on a .48 as a comparison. That's 350fps on a .2 and 226.1fps (1 decimal place) on a .48. We can already see that momentum is going to be very different, but for argument's sake...
momentum = 350 x .2 = 70 gram feet per second
momentum = 226.1 x .48 = 108.5 gram feet per second (1 decimal place)
So a heavy BB fired with the same kinetic energy as a lighter BB has more momentum (just over 50% more!). This is why when someone point blanks you with a .48 from a 1J pistol and says "stop crying, it's only 1J" is talking bollocks. Do I think we should be operating on momentum-based rules for airsoft? Hell no, that would be cancerous, but it's a consideration that I feel comes under the golden rule of "don't be a dick". However, this also goes a LONG way to explaining why heavy BBs tend to go further than lighter BBs; they simply have more momentum pushing forwards due to how physics works (the old example was if I throw a balloon vs if I throw a cricket ball with the same kinetic energy, which goes further). However, there's one last thing to consider when it comes to range and that's deceleration, as the BB is being affected by a number of things trying to slow it down and drop it to the ground, namely air resistance and gravity respectively. Hop up creates a backspin to give the BB an upwards lift to combat gravity, but combating air resistance isn't happening. I won't go into the mathematics on this as deceleration past GCSE level is really maths intensive (I would probably have to break out calculus and trigonometric functions to explain my point), but essentially an object moving at a higher velocity has more air resistance acting on it, so that BB travelling faster actually has more pushback from Mother Nature than a slower BB. Furthermore, that air resistance is going to have more effect on a lighter weight projectile as lower mass makes it easier to push back, so a combination of higher air resistance and more impactful air resistance means that a lightweight BB fired at the same energy is going to slow down and lose that energy a hell of a lot faster than a heavy projectile.
Anyway, I hope you're all still awake after that (I find it fascinating, but I know not everyone does), but now I'll move into airsoft specific phenomena like joule creep and cylinder to barrel ratio.
With AEGs, it's rare that power goes up with weight but it is possible. I couldn't explain to you in detail how the maths works out, but essentially there's a sweet spot for ammo weight with most guns and it varies dependant on inner barrel length and cylinder size. What tends to happen is that shorter barreled AEGs are more efficient with heavier ammo, but longer barreled AEGs tend to drop in power with heavier BBs due to voluming issues; the cylinder doesn't have enough air to fill the barrel so the BB starts to decelerate while it's still in the barrel, meaning that a heavier BB that comes out slower originally will start to have forces working against it (friction with the barrel and air resistance) sooner by fractions of a second, but it all affects it. It all depends on if there's enough air in the cylinder to fill the barrel. Look up cylinder to barrel ratio for a better explanation than I can give; I don't use AEGs much and they're the only guns I don't tech myself because I'm useless with gearboxes. Also, as has been said, heavier ammo typically needs more hop pressure to be applied which can also drop your power (as at the end of the day you're adding some resistance to the BB's flight path.
Assuming you have enough air volume in an AEG, or if you're using another platform like a GBB, then heavy ammo will typically cause your power to go up due to joule creep as long as you're not having to apply incredible amounts of hop to lift them. The BB will accelerate while it's in the barrel as long as there's something to push it, which for a gas gun is the gas expanding when it leaves the magazine, so a longer barreled gas rifle will have a higher power than a shorter barreled gas rifle as it has more space to accelerate before leaving the barrel; it's the same as real-steel firearms, a long barreled AR-15 will shoot better at longer range than a short barreled AR-15 assuming the same ammo due to acceleration in the barrel.
So why am I saying any of this? Well, it's the considerations part of your question. With AEGs you need to consider cylinder to barrel ratio and with gas guns you need to consider barrel length. In both you need to consider the hop setup and how much you need to apply to lift the BB and the barrel diameter also impacts power; wider = less power, tightbore = more, as there's less space for air to escape past the BB in a tightbore so it has to push the BB out to escape the inner barrel, which at the end of the day is what the gun is trying to do with all that air and is why air seal is so important for consistency, as the air will seek to escape from wherever it can.
Now in terms of the benefits, a heavier BB will tend to have a more stable trajectory, has a bit more punch to get through foliage and will retain its kinetic energy for longer, though we're talking about fractions here. Will a .32 be all that different to a .28? Not really, but will a .48 perform differently to a .2? It most certainly will but I think often times people over-estimate the difference in BB performance. Wind will still carry a .48 off to Narnia and a leaf will still deflect a .48; trust me, speaking from experience there as a bolt action enjoyer who has watched many shots through my scope go their own way because of wind or leaves in the way. Really, punching through foliage requires volume of fire as opposed to weight of BB and I think "go heavy to punch through foliage" is a false economy. Even my .48s fired at 2.3J have issues punching through foliage and I usually try to post the shots through empty spaces in the bushes rather than going through any leaves; precision over power.
Anyway, I feel like I've gone on enough about this. Thank you for coming to my TED talk on BB weight and the physics behind our hobby. In short:
- Heavier BBs fired at the same kinetic energy as lighter BBs have more momentum, which is why it hurts more getting shot by heavy BBs, even at 1J
- Faster projectiles have more air resistance acting on them
- Lighter projectiles are more affected by air resistance
- Therefore lighter BBs travelling faster both have more air resistance acting on them and are more affected by said air resistance
- This means that heavy BBs will travel further as they have more momentum, less air resistance acting on them and are less affected by that air resistance (assuming your hop can lift them)
- Joule creep will cause power to go up in gas guns with longer barrels as the BB has more room to accelerate
- Cylinder to barrel ratio affects power (and consistency) in AEGs. Heavier BBs can up the power in short barreled AEGs, but tend to drop the power in long barreled ones
- If you want the absolute maximum performance of your gun you generally want to be as close to the power limit as possible with the heaviest BB that your hop will lift
- I will still call you a dick if you run .48s in a pistol, especially if you're shooting up close