it really depends on how slow heavies actually are. If they movement speed is still pretty fast, I think heavier weapons would should slow them down a little extra. (It's one of those balance thingies)

You can see the speed of the Heavy at around 1:51-1:53 in this vid - http://www.youtube.com/watch?v=Q6phTyM65rM

Perhaps miniguns could be given a special stat buff that slows down their user. Or you could even possibly need a perk or bonus to use one. This could go for duel wielding pistols and SMGs as well.

Why would you want to slow down their users? Only Heavies can use them, and they are already the slowest bodytype. One of the advantages for playing Heavy is that they can use Heavy weapons. It doesn't seem fair to offer heavy weapons only to heavies (the slowest bodytype) and then penalize them for using them, buy making them even slower.

Slowing down Heavies who use heavy weapons (essentially, penalizing them for using an advantage of the body type) would be like having sprint meters only for Lights.