1997 Chevrolet Blazer Question: Why won't my interior lights go off and blow the fuse?

Sounds like your interior lamp module or circuit is acting up, keep in mind that if your blowing the fuse there is a short somewhere in that circuit. The fact that you say the lights dim then come back on after you blow the fuse tells me you have a short to power. This condition needs to be found and repaired as shorts to power will put unnecessary drains on your battery and can cause fires.