I would fold on the turn.
How many times have you been CRd twice by a limper?
How many of those times did they have a hand that wasnt the absolute nuts or very near to it?
How many times have you see a limper CR as a bluff? How many times have you seen them do it twice?
If he had JJ,QQ,KK then he would likely go into call down mode on the turn.
If he had AK and spiked a king, he would likely go into slowplay mode had he been bluffing
on the flop (not that limpers tend to bluff all that much)
I realise that villian is repping a very very narrow range, however I ran a quick report and of the 300K times I have seen a limper cal a raise OOP, I have only seen them CR 3% of the time.
Of that 3% their overwealming action on the turn is to bet most of these hands get to SD and they usually have the nuts so what this means is that the 3% of the time a limper CRs its almost always the nuts.
Saying that I probably wouldnt fold the flop raise, but the turn CR is just a better hand than yours.
You have a good hand, but if you held JJ preflop and the limper 3bet you would you call? We can even give this limper a 3bet % of 3%.