You don't have to be bulky to wield a sword. If it was an axe, zweihänder or halberd, sure, but a regular medieval sword weight like 1 or 2 kg (it's a bit below the weight of a bottle of water). If the MC was not able to carry it... Well, she probably has other issues. Anyway, the MC still suck at the sword; if the MC had, without explanation, physically overpowered an opponent, it would be ground to complain, but for now...
Similarly, a normal man or woman can carry 10/12 kg loads for a short time, like when cleaning, carrying groceries, stuff like that... (while complaining and moaning, certainly but still). Up until now, the MC hasn't been doing anything extremely physically taxing that would have me raise an eyebrow. Women (and men) aren't made of glass that they would shatter the second they carry something that weight more than a fork.