I've done the Muir a few times. I would want to be ultralight! Nothing big and nothing heavy!
The Southern Sierra is pretty mellow in mid summer, except for afternoon thunderstorms. It could sleet/snow, but it doesn't stick. 25 days is 10 miles/day, so you won't have to kill yourself. Your chances of ending up in some kind of long term survival situation where you would need chopping tools, or a heavy knife aren't great. No fires above 10,000', but plenty of dead stuff everywhere for one in an emergency, below timberline.
Extra food is more important than anything else you can carry! Any extra weight should go for that, not hardwear. Are you going to get resupply, or hike it all the way through??? Put on a few extra pounds before you go. I always loose a lot of weight on a long trip.
For me, an extremely light Gerber saw, a small/light multi-tool, and my Emerson CQC-12 which goes everywhere with me outdoors clipped on my pocket....just because.