I don't really like raising the turn unless you want to stack off. (which I'm assuming you don't really want to do given the concerns you expressed) You can 3bet pre I think it makes the hand a lot easier to play.
When I played 2nl I used to take villain's exact line a ton with my overpairs, (pot/pot/shove) he may just think you are another bad 2nl player calling down with any pair. I also used to shove rivers for value an insane amount (sometimes very thinly) so I think if you feel that he is a tight in line player then hes probably doing this for value and you need to fold now.
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