I just watched this episode. I think that Tyrol has probably the deeper character of Sharon's two men; Helo is not dumb, but he's perhaps not as introspective. I think that his emotional connection to Sharon and their baby is deeply important to him; also at that point, he'd been snubbed by most of his crewmates, so I can see him wanting to reinforce the connection with Sharon, and reassure himself that she at least cares about him.
I really liked Tyrol in this; he is growing through all the adversity, and finding a way to create something that brings hope to the fleet gives him a real strength.
Anyone else wonder about that little scene with Dualla and Apollo? There was some definite heat there. Billy better watch out, methinks.