Old is right, velocity will increase, up until a certain point. The 2nd poster said something to the effect that 1/2 the bullet weight would be 2x the velocity in the M1 carbine. Well, I'm pretty certain it would be extremely difficult to develop the pressure needed to launch a 55 grain bullet at 3800 feet per second from an M1. So it isn't just a simple formula/answer for the OP's question, there are many variables and factors.
Anything from a rifle moving at 3000fps requires tremendous pressure to achieve, and rounds moving close to 4000 fps are REALLY moving, and are typically specialized calibers, the WSSM's, magnums, bench rest rifle calibers - that sort of thing. As you close in on that 4000fps velocity bullets start behaving differently as well, there is mucho stuff on google if you want to read about it. An example: The .408 caliber, pretty much the gold standard for long range shooting, that or the 416, both move at around 3500 FPS with a 300 gr bullet. It takes over 65,000 PSI to get it to that 3500fps velocity, which is a crazy amount of pressure going off right next to your head. This bullet is still supersonic at 2000 meters, but much of this is due to bullet composition and tech, as well as the weight/velocity etc.