I have a Kenmore Washing machine that does agitate fully. Whenthe clothes level in the washer is very low it agitates fine. When the level is higher it appears to be agitating but it looks like it is just barely moving. It will not rotate fully.

Your agitator is likely connected to the mover by a plastic piece (the mover is the piece with the spiral that catches your clothes and moves them, not sure of the name) If the plastic piece (thrust spacer) is worn down, chipped, or stripped it will not move a heavy load. I'd check that first.