Tony watches Pepper sleep because it is his helicarrier and that means he has the privilege to do such things. He also has some psychological need to remind himself constantly that she's alive, she'd doing great. She's breathing. He saved her.

He really prefers the 'he's in charge, so he's allowed to do this stuff' angle.

It's the one that doesn't make him look like an emotionally fragile stalker, after all.

She sleeps.

His eyes are fixed on her chest, on the glowing battery between her breasts that keeps her going. The constant light probably makes it hard to sleep.