No to weighing, no to commenting on an athletes weight. EVER! I never went to a gym that weighed, but I heard plenty of comments from coaches about how fat I was and the emotional damage remains. I have a ridiculously bad body image and blame most of it on those coaches. Weight should be monitored between the athlete, her parents, and her doctor. That's it. No coach input at all. I'm okay with talking about nutrition to provide adequate fuel for your body, but the minute it crosses over to weight it's dangerous territory.
At one particular gym I had a coach ask, "What, are you looking at how fat you are?", comment that specific girls (myself included) needed extra conditioning, that I was too large to spot (I switched to another gym that did not see that as a problem), hit my stomach, the list probably goes on. After I left they commented to the coaches, one of which was my age and a friend/former-teammate that "Going to a better gym won't help her, she's too fat for anyone to spot." It made me feel like the fattest, most worthless person and I'm not sure that damage will ever go away. I just wish I had known enough to get out of there before things went as far as they did.