Such a weird line from Villain, one moment he's inviting us to stay, next one he's putting us out the front door.
If you've enough of a sample to know his SB 3B % + his Cbet % on 3B pots you should have some kind of a note on him that would help on these kinda of spots.
Would lean on folding to such sizing OTR
I don't know if this is a popular idea, but ,what about a min raise the turn (or a 2.5x raise),to induce a check on the river? The complete line that i suggest is ,3bet/fold Turn- fold to bet or check back at River