[krimson]

I know the PF play isn't why you posted the hand but I think you're brushing this off too easily as being "correct for the situation".

#1 There is a call and a raise in front of you from fishy players. They will not magically fold to your 3-bet, they will 90% likely call it down.

#2 a 3-bet increases the chances of folding out the 3 players behind you giving you the button, and isolating the fish

#3 A 3-bet decreases the odds given to the blinds, making them more likely to fold putting dead money in the pot

As a result of your cold-call you ended up getting a call from the BB, for a total of 8.5sb's (contributing 2).

Had you raised and had both players call you would have 10.5sb's in the pot (contributing 3) so essentially an extra sb up for grab.

In addition to the extra bet there is one less player in the hand, increasing your pot equity.

Obviously 3-betting is +EV even if the rest of the table left to act is tight as hell.

edit: Should also add. Since villian is playing very aggressively you could get a loose 3-way cap from him making for an even better situation.