Yeah, the little dogs do tend to be spoilt more so they have more to start trying to defend from being taken from them. Being picked up also raises their status because it is lifting them to a higher level. They belong on the dog shelf with all the other dogs.
You often find that little dogs who spend most of their time being carried are snappy and nasty with anyone who tries to touch them or come too close.

In my opinion, dogs have legs for a reason.