When I give a city to someone, it's because that city will cost me too much and gain me too little, so I give it to someone else. Then it doesn't matter if it's a burden to them or a blessing, they see it the same way irregardless.
I remember a game in which I had only 3 opponents. I built up and built up, and was no more than 2-3 turns from DoWing and cakewalking my neighbor, Tokugawa, and he asks to become my vassal. "Uhhh...... Okay." So I moved my troops into position to attack HIS neighbor, Hatshepsut, built up and built up so it would be a cakewalk, and I'm like 2-3 turns from DoWing, and SHE asks to be a vassal! "Uhhh.... Yeah, I guess that'll work." The third AI player was about as big as my two vassals combined, plus he was the last one, so I figured there was no way he'd capitulate, so I got all my stuff into position around him, captured half his cities on the turn of DoW (didn't wait long to launch this war) and next turn he wanted to capitulate. Not really a chain, but I did have one other where I had like 3 guys come to me one turn after the other, and that was pretty cool. But that's it. Apparently there's a narrow window of wanting to be a vassal, and not everyone will ask you to be a vassal, you have to check with them once in a while.