My putter grip is pretty normal. I don't see a need for a large one with my putting stroke.
My parents both have heavy-putters but my mom has a large grip now instead of the standard heavy putter grip which I think is lighter than normal. Strange feel with those putters (have not tried mom's) as there is so much weight in the grip area (rebar filled shaft at the grip or something?) that when you hit the ball, it gives a really strange feel, like you made bad contact and barely hit the ball.
Neither of them are what I would call "good putters" in general.
But, whatever they like.