Why did the teddy bear turn down dinner?
Because he was all tied up in stitches!
I'm sorry, Lin. I don't get it. One, the teddy bear isn't all tied up in stiches, is it? I mean, they have stitching, but they are not all tied up in it. Two, if a teddy bear could eat, why wouldn't it eat whether it was tied up in stitching or not?
As a punchline "Because he was all tied up in stitches" is akin to:
Why did the teddy bear turn down dinner?
Because it is an inorganic toy with no need to eat.
Because its mouth is just a piece of red yarn.
Because it doesn't like veal. (Alright, not this one)
Now, "already stuffed" is a satisfactory punchline because it is true, and "stuffed" is also used to mean having had enough to eat, so it is a mildly clever and mildly funny answer to the riddle.