B.G.
Honestly, I would give in. This is just so normal. It is so common for 3 year olds to need to be "parented to sleep." (That's what the Sears doctors call it.)
Right now, he needs to feel safe. Going to sleep at night can be very scarry for a little kid. Their imaginations are working over time. If you are there with him when he falls asleep, he can relax and calm down knowing that Mommy is there, and everything is ok.
I would let this be part of the normal routine for a few days, maybe a week. At that point, sit there for about half the time you usually do. Then get up with an excuse (laundry, dishes, whatever) and a promise to come "right back." Always come back, but gradually increase the time you're gone. After a couple of days, he'll be asleep when you do come back. It won't be that long before you're back to just kissing him goodnight and leaving.
It might take a couple of weeks, but it's totally worth it. Give it a try! He's not playing you, he really does need you right now.