You mean to carry it? Both the grav harness and hover armour give you a negative weight, which should allow a gal to carry an HMG. Grav harness and *removed spoilers* some other armours give you extra TUs too which help a bit with mobility (but grav harness has negative armor, so I wouldn't recommend it).
Firing a HMG will always take pretty much your whole turn, it's something like 90% of TUs. But the 10% left is enough to move just enough to clear a corner if you were hiding behind a building or something. You either shoot an enemy this turn, or have to think a turn ahead and get in position to fire where you expect to see enemies next turn. It's a fun thing to do.
Side note: Those weapons you don't take many of, but have a large, expensive ammo are a bit tricky to supply. Firing the HMG once per battle will lose you all the ammo at the end of the battle. If you had two HMG, you could fire both once or twice and still only lose one ammo belt because of the way OpenXCom counts bullets, realizes you spent less than one's worth, so only removes one from your stash. This means many weapons with large ammo capacities are best used a lot and/or by many soldiers, or not at all.
I've never had a battle where I had to reload an HMG, so having this size of clip is a waste. Would it be possible for the gals to figure out that taking a smaller ammo belt is better for them (lighter, and they won't run out any ways) and better logistically as well?