There is an intentional delay with the damage dealt on melee weapons. The damage won’t actually hit until the melee weapon reaches the length of it’s swing (if you stabbed with a real knife/sword, it wouldn’t damage something until it actually hit it, would it?).
Heavy attack has a longer delay, due to it dealing more damage… it takes more time to actual “charge up” and eventually hit. 
However, if it is even more delayed than it should be, this could be caused by connection lag or anything of the sorts. Not 100% sure… do you have any video demonstrating the problem you have? :s