With the usual caveats that I am clueless... there are not a lot of reasonable hands that are beating you on the turn. 33/44/34!/ JJ and J4. I guess J4 check raises on that flop, but so does X4. 44 34 or 33 - I would predict slow play.

I agree with the call here. Only a 3 or 4 can draw out, and they have 3-4 outs

Turn 3... now any 3 or 4 beats you. I think I call the river. I might even call an all-in. You can't be too afraid of a boat of 3s and 4s.