Too aggressive with KK given stack depth?

UTG +1 plays a lot of hands and raises a lot.  On a few hands where he was forced to show his cards, it turned out that he would raise with most pairs and call a lot of flops with connectors (both suited and non-suited).  Considering stack depths, was my shove over the top of his reraise too aggressive given this situation?   I hit the miracle card on the turn and won the pot but I don't think I made the correct play.   Thanks.