This can be tricky, depending on how you play the game. First, you want to maximize your strength (or bring it to 9, then get the Bobblehead). Then at level 8, get the Strong Back perk, which enables you to carry 50 more pounds of equipment, to a total of 300 pounds.
In short, there no real way to carry loads of items (power armor and everything) with just 300 If you really want to carry pretty much anything without having to worry about weight there is a mod for that. However, some people don't like using mods.