How do I increase the amount of stuff I can carry? My max is only 300.

Unless there's mods or console commands (pc only) then 300 is the maxium your carry weight will go.

Make a stash hold out of containers that don't reset them selves every 3 days. I.E. wall safes, ammunition cans, and med kits work well. When you are done with a quest, or just exploring a house or area, just fast travel back and forth to pick up all of your stuff. It can get tedious, and I did it a lot on my first few play throughs. I don't do it much now. I'm a little more picky about what I pick up now.

A good place I found was Galexy News Radio. Inside, up the right set of stairs is a row of lockers, they are non respawning and well guarded.

Or disarm/destroy the Megaton bomb.