Thanks for the responses so far.
It seems to me like you're saying that the amount of troops I can call up from my provinces depend on my income. If I have higher income, then the number of troops will go up.
The problem is, though, that I'm making 82 a month in income. As an example, in Innsbruck I can call up slightly less than 1,500 soldiers. France, by contrast, has an income of 65 per month. In Ile de France, they can call up well over 6,000 troops. Moreover, I've recently inherited Franconia, and was watching as I took over and unpaused the game. The number of troops can be called up from Franconia nosedived as soon as I took control of the region.
It's very strange that I have 208,000 manpower and a decent income (again, this is a new player's perspective) and the armies I can call up are tiny in comparison to France and even vassals like Genoa. (Genoa can call up over 7,000 troops).
I still don't understand what's going on. Am I not doing something correctly?
EDIT: I think I might have just figured it out. All of my provinces actually have very low income in comparison to their neighbors...
So, in that case, how do I improve a province's base income?