The gunnery skills have a VERY skewed effect on the different weigh classes of 'Mech. Better gunnery will hit more often, which doesn't make THAT much of a difference in an Assault battle, because most of the shots would have connected anyway. With light 'Mechs and high movement modifiers, the "snowball's chance in hell" of hitting them suddenly becomes a fairly decent shot, and speed is no longer sufficient to save the fast, light units from destruction. If you mix lights and heavies, the lighter units may serve as little more than cannon fodder against veteran and elite units.
Note, as stated, that most units cannot shoot at Range = 0. Battlemechs may perform certain physical attacks against units in the same hex, and a stomp attack against a vehicle, or a kick at a Battlemech or vehicle in an adjacent hex (Range = 1), can be a game-changer. Those much maligned piloting skills come into play here, and a 4/4 pilot can frequently kick the legs off a 4/5 challenger and win the battle.
One may laugh at the badly armed Charger 1A1, but put a 4/4 pilot into the silly thing and it's a dire threat to anything within the 8 hex range that it can reach during movement. A 16 point kick is sufficient to take a leg off of most light 'Mechs and some mediums, and will breach the armor on some heavies. Two turns with a favorable initiative roll and even a heavy opponent is generally flailing around on the ground (since you can get into the appropriate side arc to kick the damaged leg again).