Cause it's not really his kid
This is up for debate. I'll just assume it is his and she got the AIDS from sharing needles in a relapse at some point in the few years they were apart. People died quick from AIDS back then and she probably didn't have it more than a couple of years.
She knew that he was loaded and could take care of her in her last days and could take care of her boy after she died
This isn't very debatable. If you just look at her history she is Forrest's friend. She was obviously to smart for all the other rednecks in Bama and she didn't fit in with the debutante bitches, so it isn't surprising her only other option was a dumbfrick who didn't care. So she is happy to see her friend in D.C., but doesn't give much of a frick besides that. Years later, she is tired of being on drugs and being a whore so she settles down for a few months with Forrest because she knows he will take her in. Then she runs off after he starts getting too attached to her. Years after that, she finds out she's dieing and needs someone to take care of her kid. What else could she do but call on old Forrest again?
Does she suck as a person? Yes. But she really did love and care for Forrest.