Against a player who pushes all-in preflop almost every hand (but seems to fold his very worst holdings), what hands are you calling with if everyone else has folded? What about if there are limpers? Also, what's your plan if he hasn't acted yet and the actions on you?

I just played at a 25nl table with such a player and called five of his all-ins with QQ, JJ, AJo, A10s and 77 respectively. After thinking about it, I think the call with 77 is bad because very rarely will I be dominating his hand (maybe this changes if I were confident he would rebuy once he loses all his money). I'm fairly happy with the other calls. Thoughts?