I am a very out of shape person that is starting to work out on a treadmill and getting a little better.

Just a few hours ago I had to carry some heavy awkward boxes up some steps and my legs felt funny and they felt like if I kept going up the stairs with more boxes that they would give out.

Is this normal for someone who has little leg strength and obese?

It's normal for anyone, especially after exercise. Sometimes when I've done a high intensity cardio workout (i.e. running), I sometimes feel like my legs are going to give out when I get off the machine. I sit down for a few minutes and rest, and things get better.

I suppose if you're obese then it does put a lot of strain on your legs which could cause a similar situation. Keep doing the cardio and try and clean up your diet and the weight should come down which will make your legs much better. :)