Divide et Impera has a ton of interesting new countries - tiny ones, often vassals of larger powers, but sometimes just independent. (And despite the title, not all of them OPMs - other new nations that have a couple provinces aren't much easier.)
Unfortunately, I can't for the life of me do much of anything with any of them. They're all in pretty weak positions to start out with, and if I try to devour other OPMs they get that event to recruit an army larger than I can muster.
Any tips for trying to make these weaklings powerful?
yes, I've got a nice way but some (including myself) may call it an exploit/bug.
If you can survive long enough to save up some gold for spy action you can fund patriots in some near province with your culture (but owned by other culture, though I'm not sure if that is necessary). With some luck the rebels are successful and you get a province. Without the core . The rebeltype should be "patriot". Never station your army there. (since you can hardly call 2000 an army, right?) If the rebels appear there is a high chance that they will leave the province immediately without laying siege. And they will go and get for you the neighboring province with your culture. And in 2 years you will get all the provinces with your culture, just don't station your army in their way or in the "coreless" provs.
I don't think there is any miraculous way for OPMs, in their cases most depends on the ruler, a good diplomat is quite vital (diplomatic skill event that gives you 60 in one of the options, now that can fund quite a war), marriages, maybe joining HRE. Well, the rest is luck. I had one game when I united Silesia by Swidnitz-Jawor, and in the second one Bohemia ate me in one year (siege included)