You make a good point about the message that he shouldn't be reraising me light.
, so a raise is good here, but I still don't like the push.

As for the rest of the reasons, that it will be dificult to put him on a hand, etc. I can't agree here in a reraised pot in position you don't need to worry about being outplayed. Just don't fold and it will be fine.

I would probably made one more small reraise to 111 or 122. It would be difficult to him to fold here and if he does he will lose a 'dick measuring conest' (obviously he'll get the message). If he calls I'll gladly put it in on any flop without an A.