Weena is one lucky Eloi – she gets burned to death rather than eaten. The Time Traveller is relieved when he thinks the forest fire got her before the Morlocks (9.16) – and he's her friend!
Weena seems to keep getting into these dangerous situations, which the Time Traveller tries to rescue her. If that were all she was good for, she wouldn't be a very interesting character – she'd just be a prop to show off the Time Traveller's heroism (or his lack thereof).
Weena is like the other Eloi in many respects. She's not very smart. She's easily tired. She's amused by matches and frightened of the dark. She's graceful and childish.
But at the same time, Weena has her own personality. She has retained certain feelings that the other Eloi seem to have lost – gratitude, for instance. After the Time Traveller saves her from drowning, Weena keeps him company and tries to keep him safe and comfortable – in her own way. This mostly involves trying to prevent him from going underground and putting flowers in his pockets – which is what she thinks they're there for. (Weena reminds us a little bit of several cats we've known, who have thought that our shoes were made to hold mice.)
So Weena is set apart from the Eloi by her gratitude and affection for the Time Traveller. He certainly feels something for her, because around the time he realizes that the Morlocks eat the Eloi, he decides to bring her back to London (7.16). When the Time Traveller asks Weena about the Morlocks, she gets very upset and starts to cry:
They were the only tears, except my own, I ever saw in that Golden Age. When I saw them I ceased abruptly to trouble about the Morlocks, and was only concerned in banishing these signs of the human inheritance from Weena's eyes. And very soon she was smiling and clapping her hands, while I solemnly burned a match. (5.41)
Notice how in that one passage Weena is marked out as different from and similar to the other Eloi. On the one hand, only she cries, just like the Time Traveller. But notice the difference that opens up between Weena and the Time Traveller in the last line: while he's solemn, she's childishly amused by fire. (Her relation to fire is a little strange – she's amused by matches, wants to play with the bonfire [9.4], and possibly gets killed by a forest fire. It's like a PSA for fire safety.) By seeming both human and not, Weena is a reminder that some things change, but others don't. That's at least how the unnamed narrator chooses to think about her in the Epilogue.
Lastly, we have to deal with the romantic angle here. The Time Traveller and Weena give each other flowers and kisses, and all the movie versions of the novel decide to make this into a love story. Is it? Since the word that the Time Traveller applies to Weena most often (in some form) is "child," it seems like the relationship here is less romantic than affectionate or paternal. (Which doesn't prevent us from considering some sort of Time Machine / Lolita mash-up.) Check out the "Steaminess" page for more on this issue.