Some quick research has told me that anvils that couldn't be lifted by one or two people were pretty rare. Liftable anvils makes sense.
As for what happens when you log out with things over your head, I think the intended behavior is that the object tries to drop in an empty space next to you so you can still log back in without it blocking you. If there is no space it drops right at your feet if it can, and if it can't do THAT it destroys it.
I think there are two reasons they don't just stay with you while you're logged out. The devs didn't want people to be able to hide chests and such while they were offline, and they didn't want to deal with what happens when something appears under you while you're logged out AND you're carrying something. It either has to teleport with you to your homestead (something they don't want), or it has to fall at your feet and embed itself in the other object.