So why does Han decide to pay back Jabba after three years with the Rebels and an apparent decision to stay permanently?

Well, there's the obvious reason: as he says, "[T]he bounty hunter we ran into on Ord Mantell changed my mind." Jabba still wants him alive ("He's no good to me dead"), so there's still a chance that Han can pay him back and get that pesky death mark off his head.

Then again, many fanfiction authors ask, how much of a difference would that really make? He's a known associate of Luke Skywalker and Leia Organa! Vader knows who he is and probably had a grudge against him for that little incident in the Death Star trench. He'll have a death mark on his head whether he pays Jabba back or not, so why risk going to Jabba when Jabba probably wants to see him suffer more than get his money by this point? Maybe the real reason he's leaving is because something happened (or almost happened) to Leia on Ord Mantell and he can't bear to put her at unnecessary risk anymore.

That explanation never really satisfied me. For one thing, there's just no evidence. For another, if Jabba isn't making things particularly more dangerous for Han, then Jabba isn't making things particularly more dangerous for Leia either, and Han's smart enough to realize it. Finally, I think Jabba is a substantial threat. Piett's "We don't need their scum" is a good indication that the Empire doesn't often team up with bounty hunters. Bounty hunters and Imperials work in different ways and travel in different circles. There may be some overlap, but not always. So having both after you really is worse than having just one.

But his dialogue does leave things open for a second motive:

[W]hat about you need?

LEIA: I need? I don't know what you're talking about.

HAN: You probably don't.

LEIA: And what precisely am I supposed to know?

HAN: Come on! You want me to stay because of the way you feel about me.

LEIA: Yes. You're a great help to us. You're a natural leader...

HAN: No! That's not it. Come on. Aahhh -- uh huh! Come on.

LEIA: You're imagining things.

HAN: Am I? Then why are you following me? Afraid I was going to leave
without giving you a goodbye kiss?

Although if you asked him, he'd probably deny it, Han cares about Leia. And though I doubt he uses the L-word even to himself, he is aware that he wants to be in a romantic relationship with her.

Leia, on the other hand, is still in that river in Egypt. "I don't know what you're talking about." She does have some feelings for him - come one, she didn't chase him down as a representative of the Rebel leadership - but she just will not admit it to him or to herself.

How long this has been going on, we don't know, but Han is plainly getting frustrated. "You probably don't." He keeps pushing her, and not at all subtly: "You want me to stay becuase of the way you feel about me... Afraid I was going to leave without giving you a goodbye kiss?...I think you just can't bear to let a gorgeous guy like me out of your sight." He's trying everything he can think of - and still, nothing.

So maybe Han is close to giving up on Leia and is just a little bit glad he's in mortal peril and has to go lose that death mark so he won't have the constant frustration.

But it doesn't take much to convince him to stay. As soon as Leia's in danger, he runs back for her - and once they're alone (well, nearly alone...), he just goes for it and kisses her. And she finally responds.

The kiss isn't an unqualified success, however. Sure, she'll kiss him on the cheek after that and let him kiss her, but she's still pretty distant. And there's still that little sticking point:

HAN: ...we'll soon be gone.

LEIA: And then you're as good as gone, aren't you?

He doesn't deny it. Of course, he doesn't confirm it either, so maybe he looks guilty not because he's planning to leave, but because he hasn't decided and thinks that's just as bad.

It's a tough decision. Jabba is still after him, and that really is a problem. On the other hand, Leia is finally warming up to him. When will he ever get this chance again? Is it worth the risk to be with her?

Luckily for Han, in the end he doesn't have to make that decision. But one wonders what he would have chosen. Me - well, he came back every time he tried to leave before, so I think he would have stayed.