A check raise is used by the player out of position, where here they are in position (BTN). Rather than a villain check raising, it is your bet that is a donk bet. Perhaps you got confused by the 3bet.

That's a 4x raise from BTN by the way, is that their standard? If not I would just fold out from the SB.
Villain has less than a full stack, has position and raises to 4x. We have a drawing hand and are out of position, therefore I would fold preflop because we don't get enough implied odds in my opinion.
Another problem is the 3bet sizing, we need to make it bigger, if we think we can get folds, otherwise we just encourage villain to call in position. The problem there is the stack to pot ratio gets a lot smaller postflop leaving less room for making moves.

Obviously opinions can change with more information.

As played, I would check/call the flop and seriously consider folding the turn unimproved. Betting out in a 3bet pot out of position just bloats the pot and it's no surprise to get raised. As you played it, when raised it's fold time for me.

Tl;dr - I'd fold preflop without good information about BTN and BB. Just the way I'd do it this time and only my opinion.

Gl.

I think I'm 3betting bigger - 50c or so. Gives us 1.08 in the pot on the flop. Betting 75/80c flop and getting the money in.
We either get called and we jam turn, or we get raised and we can jam over the top, or we get jammed on and can call off with a stronger hand than we normally have in this situation.