its not a continuation bet when you have a hand, it is a value bet. why would you check the turn? unless your hoping he will fire at you sensing weakness. not very good if your reasoning is your letting him "catch up". The reason for this is that #1 if he misses on the river, you will not get anything more out of him and #2 he called your flop bet, what makes you think he will not call a turn bet.

the turn, i would fire out another 180 (trying to feign weakness by not increasing the bet), but i can also see throwing out a 1/3 or 1/2 pot bet (this may scare him away though).