I think you are indeed overthinking this. The term "love" when said to a person is just a term some people use. I do. I say that to a lot of people I am close with. I don't use it exclusively to them but nonetheless. Doesn't matter the gender either.
It is entirely possible she is using it as a term of endearment as well. There is really no way to tell. We are all just guessing at this point. There would be some other clear signs she was interested other than just calling you "love".
Are there signs of flirting? That is what I would be looking for if I were you. If she doesn't pursue any further than just calling you that, I would leave it be. She is, after all, going to please members of the gym.
That is her job. She isn't going to come off as rude or possibly make members upset. That is why I believe this is a classic overthink. Sorry, just my view on it.
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When I was young I worked at a bar. There was an older bar tender that did a favor for one of our waitresses and she said, "oh, thanks, Kevin! I love you"! He took it literal. He was married and she had a boyfriend. Long story short, he ended up getting fired and banned from the bar for harassment. Not saying you would do that but don't take her words literal.
It could mean a number of things. Everything from a form of condescension to actual feelings. You should spend some more time talking to her to see if you get any clues.
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I wouldn't assume it just from that. Does she ask you questions to get to know you personally?
That means absolutely nothing English women say that a lot
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