[Lloyd]

Obviously, there's no magical formula. If I'm up against multiple opponents I often don't even take a stab at a pot with a middle pair. If it's one opponent, more important then what you have is what they probably have and how their hand range fits in with the flop. If you're heads up and flop middle pair, and think the flop might have missed your opponent, you have a few options. You can check with the intention of either raising or calling and leading the turn. Or you can lead out. If you lead out you'll often be raised. I've been check-calling and leading the turn recently as that's often how I'd play a set. Much of your decision is also based around stack sizes. I certainly wouldn't want to invest a big portion of my stack with a middle pair if I wasn't pretty sure I had the best hand. I might lead out on the flop and see what happens. Anyway, just some random thoughts.

First Hand: You don't just have middle pair here. You have middle pair with the nut flush draw. This is a strong hand. You have 9 good outs and often 5 more. You're usually 50/50 versus a hand like KQ/QJ/KK. When the BB makes that weak little bet I'd go ahead and raise. You might win the pot right then. If not, you'll likely have an option of a free card on the turn. Calling isn't horrible since you're getting good odds but with that bet I think you can win it with a decent size raise.

Second Hand: I'm presuming this is four handed. If not, fold AT unless you think your opponent is on a steal. In a full game you should not usually be re-raising an UTG raise with AT. If it's four handed things change. Since UTG is shortstacked you either have to fold or push. AT four handed is a strong hand and I would push pre-flop unless I had a good read that his small raise meant something big. Basically, with his stack size, you're entire decision should be made pre-flop.