i probably wouldn't 3-bet, unless you are intending to 5-bet shove if he 4-bets. if he's reeeeally over-aggro, it's probably wouldn't be too bad actually. wait just realised you limped, dislike.
if he really is calling all 3-bets and not folding pairs postflop then i'd probably just go bet, bet, bet...but i also don't mind checking back the flop or turn or river. might be slightly thin to bet all 3, but if he's as loose as you've described it's probably fine. if you do check one of the streets, you really have to be betting the other 2.
It works really well it puts the pressure back on them post flop.
what pressure did you put on them postflop? just bet!