You think a teenage girl shouldn't be able to climb a few flights of stairs? When I worked in the ship yards I worked with men who needed hip and knee replacements and they were climbing scafholding and dock steps all day...
Whether you or I think a teenage girl should be able to climb a few flights of stairs is irrelevant. It isn't your responsibility to tell her that she needs to climb stairs to become healthier unless she asks you for health advice, which in this case was unlikely. If the elevator is out of service and you simply direct her to the stairs as an option, you are not being rude. You are being helpful.
I climb stairs and exercise regularly, despite having a somewhat bum knee. Likewise what the dock workers you knew did is not relevant and does not grant you permission to offer health advice to the teenager. If she were concerned about her health, she probably would not be obese.