I just started up Skyrim today and I can't move normal. I move like I got too much stuff carrying around but it clearly says weight is 300/320.

I'm level 15 and have played 23 hours.

Press the "toogle run/walk" button? default is capslock, I believe.

oops. double-tap.

Yeah, you do slow down as your load becomes heavier. Just like real life. This is normal behaviour. But Skyrim still lets you run until you hit that maximum limit. Drop a lot of your load then you'll get much quicker when moving.

I think I had capslock on. I turn it off and see what happens.