As R.L said, the end result will depend on the gun. But as a rule .12g BBs wildly unstable/inaccurate; heavier BBs may not shoot "straighter" (if you're shooting 315fps with .12g you're low on power, for any number of reasons) but it should at least shoot a bit more consistently.
.20g is probably your best bet to get similar performance with more consistency. .25g or heavier may be too heavy for you to really benefit from, specially if the hop-up isn't adjustable (?); If it is, you might benefit. See if there's another player(s) in your area you can bum a few heavier weight BBs from (and fill out your location in your profile)