This was the marking in an etude I was playing once in a lesson. I took it to mean what it looked like -- "graveness" -- so I played the etude with a sort of heavy sounding dirge style. However, when you look gravita up, the definition is "with gravity or majesty"; my problem with this always was that those two words mean quite different things... but do they really?
Gravity, aside from being that thing that keeps us all on the ground, means something like 'serious behavior'. My American Heritage Dictionary tells me that one of the definitions is 'solemnity or dignity of manner'. One of majesty's definitions in the same dictionary is, 'r
So my advice is that if you ever encounter gravita as a musical annotation, tread carefully. No, really; each note should be deliberately placed, like a queen walking to her coronation.