There's Energy Weapons, Guns, Melee, and Unarmed... what about heavy weapons? What affects their stats?

The Guns skill covers both small guns and big guns.
Heavy weapons also have a cap on how strong you need to be to use them properly so make sure you have high enough Strength for that.

'Heavy' weapons fall under the relevant weapon-type skill--Minigun is a Gun, Laser Gatling is an Energy Weapon, missile launcher is covered by Explosives, etc. Heavy weapons have a high Strength threshold to use them effectively--if your Strength is too low, your accuracy will suffer (or your speed with melee weapons).

Cheers

explosives covers rocket launchers and the fat man, guns covers miniguns ... read the in game descriptions of "explosives" and you'll see..

No, it doesn't.
Why can't anyone get this right.
Big Guns is not merged with Small Guns.
It was dissected into all ranged combat skill.
Guns got Minigun.
Energy Weapons got Incinerator, Flamer and Gatling Laser.
Explosives got Missile Launcher and Fatman.