My mixed thoughts on the different weapon classes:
* Heavy weapons. Made to lay down a heavy rain of fire with accuracy, even at distance. The trade-off is weight and mobility. Good for defense of strong points. My suggestion: Make them powerful, but wildly inaccurate if fired while standing. If fired crouched (which is as close to prone as we get), very accurate. Also, make it cheap in TU's when crouched.
* Sniper guns. Not much more powerful than any other rifle if one looks at the ballistics, but add some to the damage anyway, as they do tend to get more accurate hits. The same applies as for heavy weapons, require crouched to be accurate. Relatively expensive in TU's.
* Assault rifle. The jack of all trades. A trade-off between range, mobility and firepower. Gives decent accuracy when standing, decent damage and decent TU usage.
* Submachinegun. The nimble gun, the little brother of the assault rifle. Less damage than an assault rifle, less range. However, more accurate when standing, and uses much less TU's, so it's good for close quarters indoors combat.
* Pistol. Really not very useful if you have a working primary weapon. Quicker (in TU's) than the submachinegun, but less accurate, slower rate of fire, less damage.
* Grenade launcher. To launch lots of firepower at a distance, even lobbing over obstacles. Good when you don't care about accuracy and just want to do much damage to an area. Needs much better range, more powerful ammo (bigger blast), but also needs crouching for good accuracy. Even so, the grenades should not be too accurate, especially not on auto. Give them a nice spread.
* Rocket launcher. Basically, like the sniper, but with more punch and with a big blast. Good to accurately take out tough targets. Slower (more TU's).
* Knife. Seldom used as a weapon, more used as a tool.
* Grenades. Much like the grenade launcher, but with shorter range. Range is even shorter if crouched. They also need to be a bit more powerful.
* Smoke grenades. To cover an advance or retreat. Needs more area and more effective smoke.
Apply these guidelines on alien weapons as well, as applicable.
Note how I've used the standing/crouched as a way to give each weapon their own distinct usage. I know prone is not on the plan at the moment, but it would further enhance the possibilities to make the weapons more different.
In general, make the weapons different, so that your tactics will dictate which weapon to use. Avoid getting stuck in a watered down "everything is the same" balanced system.