it'll be pretty hard for him to have worse trips when we have quads. also we don't mind giving them two outs each to hit their full houses if they have pocket pairs.
The reason we need to raise for value here is because this is an excellent spot to bluff and we should be doing so frequently when given the opportunity, at least if villains are the type to give us credit in these spots.
I think a more interesting question is what hands from our flatting range should we be turning into bluffs here?
A player who overflats in this spot with AQ is simply a bad player.
Huge value to be made right now before the board flushes, simply a good bluffing spot you could squeeze bluff in position with.
You can make a play with so many bluffs/so many Q, this spot is like printing money, whether you're bluffing or have trips TK you just can exploit the other players and make the pot big in later streets with the position and making them make huge mistakes (bad calls or lay down value hands to a third barrel bluff eg) because of the deepitude of the stacks
lol, i was in this exact situation when i lost the biggest hand in my poker career. (my AQ vs 44).
anyway, like others have said, this is an easy flop raise. the best part is that it looks FOS, they might not even put you on a Q and try to play back. if they DO have a Q, get money in the pot before a diamond crushes the action.