We're currently playing Kentucky 1800 and Ammerland in our concert band and my director wants me to play much stronger, but i'm not able to. I squeak if I try to play stronger, and I even have to puff my cheeks to keep the low note alive, any help?

It sounds like your reed's tip opening is too closed. Playing on a "closed" reed makes a thin, soft sound, and you probably will have trouble getting your low notes. Try opening the tip a little by taking a pair of needle-nosed pliers and very gently squeezing the sides of the wire closest to the end of the reed where you blow. (This is called the first wire) Don't squeeze much, just enough to make the tiniest bit of change to the tip opening. Then try it and see if you made a difference. If you do it too much so that it won't blow at all, just reduce it a little by squeezing with the pliers on the top and bottom of the reed to get it back more toward where it was.

What is better, a thinner or thicker reed for volume? and where should it be thicker or thinner?

As always it is most likely to be a combination of factors.

The bassoon could be leaking - checking that the whisper key fully closes is the first thing to look at.

Then it could be a combination of reed, the amount of reed in the mouth, breath support & lip pressure. Get your bassoon teacher or at least an experienced woodwind person to help - doing this sort of thing on line is like expecting your doctor to come up with an on line diagnosois without seeing you.

Also compared to other instruments in a concert band the basoon is quiet & there is frequently a problem of balance, depending on the arrangement, even with experienced players.