I'm glad they didn't give her a rapier because rapiers are NOT LIGHT and would be a bad pick for a nerdy women like her, or any woman for that matter.
What are you talking about? How is 1kg/2lb not light?
2.5lb average is heavy for a one-handed sword. It's not light for sword standards. However it doesn't require a lot of strength properly wield a sword, it's mostly about being physically fit and being skilled. In fact rapier is probably one of the better swords for a weaker person to use because there is much less parrying involved, as well as no half-swording which is basically wrestling in a way.
It's not
lighter than the average short sword, but 1-1.1kg is definitely light (in absolute terms). 2.5lb is not heavy for a sword, though.
Also, a rapier doesn't need strength, but it requires a lot of wrist and doesn't offer much protection, so it's not the best weapon for a "nerdy woman". A light polearm would be much better overall, and also easier to use. In fact, something like a naginata would be a much better fit for her weeby design.