Uhhh, yes, EVERYTHING about this situation is bizarre. The woman who approached you was totally in the wrong. It would've been okay if she'd asked you where you shop. But to EXPECT you to give your clothing to someone else, just because you two might have similar sizes, is ALL kinds of presumptuous, wrongheaded, and rude. Frankly, I think this lady owed you an explanation about why she herself wasn't buying these clothes for her friend.
This raises a larger issue though that peeves me: this idea that people who have nice things don't deserve to keep them and should therefore give them away so that a different person can have the nice thing instead. As if the person who originally holds it AUTOMATICALLY is less worthy of enjoying it. Your story vaguely reminds me of all the shit I used to get once upon a time when my hair was down to my hips and very thick; I can't even tell you how many people insisted that I should cut it off and give it away to someone else who wanted hair instead. I used to think, "Why is it so wrong for me to have my hair? If you want to see hair donated, why don't you grow yours and donate that?" I heard stuff like that so many times that it gave me a complex. The woman in your story makes me feel the same way: why would she simply expect you to give away your own clothes, instead of providing clothes herself? As if you don't deserve yours. So weird. Some people have zero tact.
If you have clothes that you feel good about giving away to her, by all means, that's kind, but you can also just give her a gift card to Torrid instead — i.e., on principle, keeping your own clothes. There's no wrong answer here, though, so it's just an idea. I'm sorry you had to deal with this, but you handled it with grace.