Katniss in the Hunger Games survives through her feigned loved for Peeta throughout the hunger games. Her survival depends on her sponsors, and sponsors are willing to give more with every kiss she lays upon Peeta. With it comes to the time where Peeta must die for Katniss to win, Katniss decides to eat deadly blueberries with Peeta so that no one wins. Imagine is no one told them to stop. There would only be tragic figures at the end. At that moment, the contemporary viewer of the film had great admiration for Katniss to sacrifice herself for "love". Her "love" confused her, however, and almost ended up killing her. Without the love interest, she would viewed the same as the other competitors- a ruthless, killing machine who the human condition doesn't apply to. But with statements such as, "I couldn't imagine myself without him", it highlights both love as a method of appeal and a weakness.
Buffy's story is an even more direct application of this. She goes about slayer every vampire than comes near here. Angel poses a more powerful challenge to her because she loves him. Angel stated that to beat Buffy with force is useless. To defeat her, you must love her. It was shown that Buffy is very susceptible to this because she refuses to kill him at the end of the episode "Innocence". If he was just another vampire to her, he would've been dead and have no potential to pose further problems to her. However, because she still has feelings for him, she decided to have mercy on him.
Now, I'm not saying that love by itself is weakness. For many people, it can be a source of strength. Lots of relationship are founded on the concept of love. However as a superheorine, being in love (especially with an enemy) would pose more of an liability than an asset.