While binary size could certainly be a factor in a good deal of embedded environments, we also need to look at the resource requirements of the binary in question as well.
Sqlite doesn't need too much more memory than what its binary needs whereas with postgresql, you need all sorts of bells and whistles just to get the database system to boot.
Well, sure, sqllite is smaller than postgres, but database system performance is largely dictated by the size of the buffer cache. For something like a configuration database (a great use of sqllite) this does not matter. But for more than a very modest amount of data more memory for buffers will benefit both postgresql and sqllite.
Anyway, not trying to make the case that postgresql is small compared to sqllite, it obviously isn't, just wanted to point out that it's not _that_ big either.
Sqlite doesn't need too much more memory than what its binary needs whereas with postgresql, you need all sorts of bells and whistles just to get the database system to boot.