I'd go with keeping a stash of speedloaders at chrono with the common weights, ask the player their weight and stuff a few of whatever they say in there.
Alternate version, i once made a device for extracting 10bb's from a magazine, think a stub of inner barrel slightly turned down at one end and a pin stuck in the other. Its original purpose was to releive midcap syndrome but such a device could easily be used to extract [known number of bb's] and weigh them.
I'd go with keeping a stash of speedloaders at chrono with the common weights, ask the player their weight and stuff a few of whatever they say in there.
Yup, my local CQB sites do that, loaded with 0.2g, with a maximum site weight of 0.25g, so it's reasonable on the face of it.
However, what it doesn't control for is when some clever-dickhead is intending to rock 0.4g in his HPA'd m4-mag Franken-Cappa, knowing that it'll chrono much lower with 0.2g and that the chances of being caught are essentially nil. I lost a fingernail to what I'm convinced was that scenario.
There's no perfect solution, but if everyone was informed and honest, then we wouldn't need chrono. If you're going to do it, and do it for safety reasons, you might as well do it properly, and on the precautionary principle.
Unfortunately I think the only way to ensure nobody is cheating the chrono would be to only allow 1 weight bought on site, however I'm sure I'm not the the only one who'd avoid a site with such rules
The only way to police that is to test in game. Do that, do it a lot, and many of these issues will get caught. Don't do it, and whatever you did it at the start of the day was just theatre.