1. you have two of the aces which removes some of the a-high bluffs he could have.
2. there is a "stationy reg" in the BB who BTN is unlikely to try to bluff.
obv I don't know his range completly, but I think it is more important that we don't have the Ad, because now he is able to have Ax-fds which he is raising the flop with. I don't think he's going to have to many complete airballs in his range, because of point 2
3. BTN is more likely to flat with draws, to invite the BB to overcall.
if BB wouldn't be that cally, it would make sense for him to just call. however, BB is a station, so BTN is able to raise and he can keep BB in.
4. It is not likely that you are cbetting light in a 3-way pot (meaning BTN should believe he does not have much fold equity, meaning his raise is probably for value, which means he probably beats AQ, which means he probably has a set or possibly Q7s).
I think hero should cbet this board with a high frequency, because both players will fold very often.
5. The fact that BB overcalls means there are more flush draws in BB's range which means there are less flush draws in BTN's range.
That's not completly true. BB will call with his Qx hands, too. So if he has a Qx hand, BTN is more likely to have a draw, but if BB has a draw then BTN obv is more likely to have a real hand. In general I think BB will show up with AQ/KQ here more often then with a draw (I think even he will fold JTdd on the flop)
I think the correct play should be to call the flop raise, fold to a BTN bet on the turn (after the read you have on BB, BTN shouldn't bluff the turn vs 2 player in this spot, so I think his range is to strong at this point if he bets), and if checked through on the turn I would call a bet from BB or vbet if he checks.
I quoted myself here, because I think overall that's the best way to play your hand. If both(!) players really care about image then the b/3b flop line might become interesting, but tbh, I don't think that this is true. Most of the players just play their game, might sound shocking, but so far I believe it is true, because most players just want to grind their 4k hands per day and try to avoid tough decissions, even at nl400. Of course there are a lot of players who adjust pretty well, but I think those aren't the norm