I think its a intressting question, but i think u need to specify a bit more

3bet or singleraised potts? flopps, turns or rivers? where are u facing this difficulties most often and were to feel like u r leaking? 

//isildroon

In single raised pots, i dont know how I should construct my cbetting range against guys like this.

If you're talking about flop x/r's I would widen my checking range and c-bet a more polarized range. If the villain is going to stab a lot of turns after you check you can create a merged turn raising range and go from there. Phil has made some excellent concept videos on raising turns I'd highly recommend. 

Yes thats right flop c/r.

How big would you estimate your cbet range would be vs named playstyle.

And what kind of hands would you check back. Second pairs with backdoors or?

Well i kind of understand what type of players u mean, its pretty hard to play back vs when being pretty unfamiliar with it. With out using any like rangetools or stuff i think i can give u sort of a mental note of how to play vs this sort of guys. 

Like every flopp u peel of as pfr vs a call, just look how well connected u r to the board and how u would play back at a cr, and like everything that will be *tough* playing back vs a c/r with u can just checkback. Mostly like openenders + a bad pair, or like bad fd's + gutters or a bottom pair. But even tho we checkback tons, it wont mean we will give up much just cause we check more, we just change approach 

for ex checking back KJ57xxxx on QT5ss or checking back your T86s4s on J92ss

So u construct ur betting range with strong hands, blockers that can 3b a c/r and some hands with some potential to improve on the turn  but have no problem folding to a c/r on the flopp. 

Try to se how he react to small 3b's on flopp as well, if he folds much or if he starts to spew. Pretty interesting. 

Paired boards is almost always the toughest vs this sort of guys, so u can prob construct ranges there as well on like a 554xxx board i would prob check back my like overpairs, wraps, and stuff. Bett som air and your 5xxx combos, throw in some hands that can call a cr with some implieds like 2paired  hands with gutters.   (ex.6688)

This means u will hit the turn with a pretty wide range and will have to play it a lot different than your std, since we check back tons of openenders, fd's u r going to be able to raise turn a ton IP and repp rly wide every time a flush hit and he leads i would prob call a little depending on  how he seem to play river and just stab at the river. 

In short, that is like my plan 1 adjustment when playing a opp that c/r tons. 

A couple of additional points: 

1) Accept that on boards that are hard to hit, you can't get away with betting a lot vs a strong opponent (paired or monotone boards being the typical ones). That's how it should be, since it doesn't make sense (game theory wise) for a lot of big pots to get built when both players have weak ranges. You can go the bluff-rebluff route and try to be one step ahead, but that's a hard game to play well. Or you can just check more and play smaller pots. 

2) Think about the implications for his check-call range. If he check-raises all his best hands and a lot of pretty good hands, he could end up with a c/c range that can be exploited on future streets by barreling a lot.