When my 3 yo DS wakes up at night, I've found it works best to be very sympathetic to whatever he's wanting--even if I think it's ridiculous. Last night he wanted to hug an empty plastic drinking cup while in bed, like it was a teddy bear. Well... okay, kiddo.
Since I'm not superhuman, I do get crabby some nights. But funnily enough, the night waking has decreased since I started concentrating on being really nice about it. It's the opposite of what I expected... but hey, I'll take it! I think that knowing he is able to get a nice, warm hug if he needs it--without being scolded--makes him sleep easier.
Have you been able to discern whether or not his requests are actually about what he says he wants? Often when kids this age are upset, they will start spouting off a bunch of random stuff. Especially if he's tired and disoriented, he may not actually be communicating what he needs. (And, obviously, if these are half-awake night terrors and not true tantrums, it's a whole 'nother ball game.)
Did you used to sleep with him before the baby came along?
I know in my house, daddy is simply no replacement for mama. His affections are appreciated in addition to mine, but never instead of. If DP were to sleep right next to DS, I am sure DS would still need me to come in and hug him myself. I didn't really like that at first, but now that I've resigned myself to it, I am rather flattered.