I play full-ring. However the 1st 4 seats folded here's what I would do.

Pre-flop. Raise more. I find myself in the same situation often. You have a decent hand and want to make a decent raise. Then somebody comes in with a mini-raise ahead of you. I think you should keep measure your raise so the pot odds for anyone calling behind you are aproximately what they would have been if instead of a mini-raiser we have 2 limpers. 4+1BB/limper = 6BB. Say $3 or at least $2.50.

Flop. Raise more. At least 2x the original raise, you have good hand. As played, maybe I call the 3-bet. But I'm definitely out of there by the turn. Smells a bit like a set to me.