Weena is the only representative of the Eloi that the Time Traveler becomes very familiar with. She represents all that is good and bad about this future race of people that is bred like cattle by the Morlocks. It is through observing her behavior that the Time Traveler learns about the relationship between the Morlocks and the Eloi.
In the story, Wells only gives names to characters that are important, and Weena is one of them. We are given an emotional attachment to Weena and begin to care about the Eloi through her. Without her we might not care enough about the Eloi or what the Time Traveler tries to do, and the story would not have the emotional impact that it has.