In Speak, what is Heather's resolution?

In Speak, Heather's resolution is to find social acceptance.

Heather is new to Merryweather High School.  She has relocated to Syracuse from Ohio.  She befriends Melinda because she is new, cannot find anyone else, and desperately seeks social acceptance.  Early on in their friendship, Heather lays out her "plan" to establish popularity, much to Melinda's horror:

Heather hops on the treadmill and resumes scheming. She isn't finished with her survey of Merryweather's social scene, but she thinks the International Club and the Select Chorus will be a good place to start. Maybe we can try out for the musical. I turn on the television and eat her popcorn.

After surrendering herself to the school spirit of pep rallies and the newspaper, Heather's resolve to find social acceptance leads her to join "the Marthas."  She becomes "a social member on probation" in order to socially establish herself.  Endearing herself to the Marthas is difficult.  She has to enlist Melinda's help to make posters for the canned food drive and other tasks because failure would mean excommunication. However, Heather makes these sacrifices because of her desire to be accepted.

As the year progresses, Heather's resolve for social acceptance leads her to sever her friendship with Melinda. Social advancement is her justification:

This is really awkward. I mean, how do you say something like this? No matter what . . . no, I don't want to say that. I mean, we kind of paired up at the beginning of the year when I was new and didn't know anyone and that was really, really sweet of you, but I think it's time for us both to admit that we . . . just. . . are . . . very . . . different.

Heather's resolution towards social acceptance can be seen in how she "walks to the Martha table" and allows herself to be "swallowed whole" while "never looking back" at Melinda.  Heather's fervor towards the resolution of social acceptance is intense.  She does not see her actions towards Melinda as disloyal.  She simply sees it as part of the sacrifice needed to be popular.