I played a game recently as Poland and kept getting week worthless heirs.

I kept a lvl 4 assasin handy to off them regularly. Eventually I created a civil war by killing all my direct heirs and fought a civil war which I would rather not have.

Opportunists stole much of my favourite land. 100 years later I had retaken all, but had to continually maintain large armies in the Balkans because "opportunists" die hard.

Dealing with a weakling king would have easier. I could have left him in Warsaw to rot while my many capable generals take care of the non clerical tasks of governing.

Best cure for weakling heirs, and this is just an observation. But significant empire expansion and improvement will do the task. When you let the nation get stagnant your heirs tend to be uninteresting. Even if you are doing well as a whole.

Build, cultivate, and conquer.

Oh, and don't be afraid to slice your sons throat if you want to insure he doesn't succeed you. Just keep one in reserve in case you slip in the tub.