Its relevant if your opponent can hand read. By checking back the flop you've basically said to your opponent "hey i dont have a set, a straight, two pair or flush draw on this flop - but i do have a hand with some showdown value" - then you bet the turn your opponent should know you can't have a very good hand so they should be more inclined to a) bluff and less inclined to b) massively reraise all in with a strong hand. Also if villain had a strong hand i'd expect him to lead the turn as quite often your'e going to check back turn.
Having said all this its difficult to for him to have too many bluffs here - I dont know what level your opponent is working on - i guess he would jam some strong vulnerable hands on the turn but i'd expect him to bet these himself.
Basically in a cash game i'm pretty much never folding top pair with these pot stack ratios let alone two pair - obvs tournaments are different but when in doubt i fall back on basics similar to what Matt said you have two pair in a 3 bet pot with a psr of about 2.5/1.
^Good post