raise flop bigger, say to 0.30 which would then be roughly the size of the pot. The actual bet you made was only half of what was already in the pot. Then you can over bet the pot slightly on the tun to say $1 ( or even at 2nl he may even just call a shove). Pot is going to be $2.80 ish. On the river, If he's still in and shoves you will then have $2.37 to call.
I think I'd then end up calling in this situation , as with his stats, if he had an A he'd probably have reraised you pre.
As played is this a normal action for him , or is he acting out of normal