Re: Weak battery causing blown fuse??
The starter motor itself bypasses the fuse, however, the starter RELAY TRIGGER, energized thru the ignition switch in the start/crank position is drawn thru the main fuse.
A slightly poor connection causes voltage to drop but also causes amperage to raise and will blow the fuse. A low battery can mimic this, charge the battery and take it in to NAPA or somewhere to be Load tested to be sure it is not contributing to your problem.
Test the starter trigger wire with a volt meter at the ignition switch while cranking, then test again at the starter relay during cranking.
Compare these reading to battery voltage as well as battery voltage measured at the ignition switch before and during cranking.
You are looking to find where the voltage drop occurs. Once isolated then start backtracking the path, cleaning and tightening all connections.
Also check for adequate grounding of the starter relay.