Is it because the sweet spot gets wider or because the picks become harder to break?
The sweet spot gets wider, I suspect by a percent roughly equal (or at least proportional) to your skill. So on master locks there's not a big difference, because 1even 200% of "pretty freaking small" is still "rather annoyingly small".
But yeah, my Argonian mercinary has a 67 lockpicking, and master locks are only a little bit easier than they were out of the gate. Lower grade locks, on the other hand, are now much easier. And no, I have no perks; blowing 5 lockpicks on a master grade lock isn't a big deal, although it seems more and more locks are master grade now- maybe they level?
Anyhow, picking harder locks is a good way to level lockpicking. If you need lockpicks, clearing bandits out of forts tends to net a fair number.
In a way, picking a lock is a lot like the "higher / lower" number guessing game. If you get it to move a little, you know the sweet spot is close, so you try a bit on either side of that, see if it moves more, and if you went to far you try between those two... basically just a numbers game. A sweet spot half as big should only take one extra pick, if you can cut the known "not sweet" zone in half with each pick.