I don't disagree that it's close between checking and raising with your holding in the BB. You didn't mention the position of the limpers, i.e. the later, the wider, and any of their images/tendencies. But on face value, doesn't seem like anyone is super strong, including your main opponent in the SB - yes, he would have to be super strong to raise the field and knowing he's playing OOP (from the absolute worst position) for the rest of the hand.
Scenario 1:
You raise PF from BB and 2 out of three or all three limpers call; SB is priced to call all but the very worst hands he completed with prior to your raise. Pot 8-10BB*. Villain in SB most likely checks to you with all his holdings ranging from super strong to super weak, i.e. a hand he would lead into you and the field with in a limped pot might not look so good now. C-betting with top pair isn't unreasonable, especially against a field of limp callers; folds to V1 in SB who calls.
On the turn, pot is 10-12BB. With the addition of a BD FD, you can go either way as you now have additional equity, but betting for value if checked to is pretty thin and your hand unimproved on the river is too weak to then call down river if V1 check raises you on turn - more optimal to check back turn. Board is highly connected and V1's holdings can include a lot of two pair combos that now might be suspect in a raised pot, but definitely can be bet for value in unraised pot. Majority of LHE players check call flop with sets, especially if it winds up HU and look to check raise on later streets for big(ger) bets. Taking free card in IP gets you to the river fairly cheap - 3BB for all five cards and your holding has showdown value if V1 checks river to you as well.
Unimproved at the river and V1 leads, you'd be getting 6:1 or 7:1 odds on a call which means you don't need to be right a whole lot of the time to still be profitable (~14% at worst?). Only if you're certain or near certain that you're beat is it a fold...and I still have a hard time giving up 14% equity against all but the toughest opponents.
Improved to flush is no brainer regardless of whether V1 leads or check calls - bet or raise for value! Improve to 2P, definitely calling any lead bet by V1 - top and bottom may not be strong enough to raise for value, but too strong to fold. Thinnest of values to bet top and bottom 2P if checked to, and has to be disciplined fold if then check-raised on river.
If river is 9, or J still calling any lead bet by V1 and otherwise checking behind - way too thin to value bet your pair of aces with board pair, but a lot of other 2P combos become counterfeited and your top pair which might be a little under-repped with turn check that can snap off 2nd pair 2P combo. Chop is also not out of the realm of possibility as V1 shouldn't be holding AK or AQ due to his lack of PF raise, despite bad position. Still profit 4+ BB
Scenario 2:
As played, you're still getting 6.5:1 odds on a call and still only need around ~15% equity, but if you factor in what you regard as your opponent tendencies a fold is fine if you can accept the possibility of maybe being bluffed and/or don't feel you have to be calling station otherwise.
A semi-bluff raise on the come for your turned BD FD wouldn't be the worst thing. V1 can only 3! OOP with 2P+ of which one pair almost has to be top pair, meaning his having the J
is the only blocker holding he can have, you're still live to 8 other clean outs or he has set of J's as AA and KK would mostly want to raise for value PF despite their bad position. Call turn 3! with plans to auto fold if unimproved, again BD FD coming in is no-brainer; an ace or three is mandatory call - not strong enough to raise and not strong enough to bet for value if checked to, but too strong to fold. Same goes for any pairing river of 8,9, or J. Folding to any lead bet if K pairs on river.
If V1 flat calls turn raise, then outcome (#BB bet/won) is nearly the same if when unimproved as all but the most expert/tough LHE players will dare bet into you on the river with holding that are also unimproved. If you improved to 2P with 3 or trips with ace still flat call if V1 should still decide to lead river. A lead bet from V1 on the river with this actual card after flatting your turn raise is an auto fold.
At 4/8 levels I just don't see very often the caliber of player who is willing to entertain the variety of other possibilites. They only think on Level 1 - What is my hand? Even the nittiest of nits at 4/8 LHE don't often think this through.
* I use BB to denote Big Blinds as opposed to Big Bets, which would be two big blinds.