I have my girls wear ankle weights when we work out. If you buy the ones with the adjustable velcro strap you can even wear them around your stomach. Personally, I like challenging them and adding the extra weight. If they can do the exercises correctly then I think it's a good idea.
I was not completely asking personally for my own little one, I was curious just in general. I once read a comment from Shawn Johnson. She said that her coaches do not allow the gymnasts to work out with weights so I just assumed there was a reason, and then I noticed in our gym the higher level gymnasts have always used a round free weight (one weight w/2 handles)... only recently our coaches have had our group of girls work out with the weights in between other conditioning skills - they all lift a 10 lb x's 10, straight arms over their head, and then go to other skills and return to the station and repeat 10lb x 10 again, but I requested my dd not participate because she only weighs 33lbs - 10lbs seemed like a lot. I just wondered how different coaches felt about their students using weights.
*** even though she can lift her 33lb self, but the weight bothered me - what would the difference be?
I think you are wise to have her skip it. Based on her size and weight, 10 pounds in free weights is too much for shoulder presses. It's not that she can't lift that amount of weight but controlling free weights can be difficult for a young child with no experience lifting them, particularly if there is nobody spotting her. It's easy to lose control of the weight and bonk yourself in the head or twist your arm in a funny direction. I have a lot of experience with weights, both machines and free weights and you need close supervision when learning to lift weights. It's easy to hurt yourself, particularly with free weights, which don't have any sort of built in control mechanism like a machine does. I think the risks outweigh the benefits, which can just as easily be obtained from handstand pushups. My 2 cents!
I think Meg has the right idea. Using weights should be determined more by the size and age of the gymnast. There are lots of strength drills that can be done without using weights and get good results.
My daughter is now just starting to use a weighted ball in her strength work, but only 1-2x/week. They work in pairs so the other gymnast can help them control it a little. Also these girls range in age from 11-13. For the most part our compulsory level girls don't use weights.
As a gymnast I enjoyed using weights to do my strength because it added to the challenge. In college I also enjoyed doing the weight lifting portion of our strength. I like using ankle weights in the gym during practice.
We are so careful at our gym, both when I'm training (trampoline and gym) and coaching. Rules are:
Only JNR/SNR international need worry about weight train (i.e. gymnasium)
No trampolinists under 12 using free weights, specifically above 2kg.
No jumping anywhere whilst wearing weights (floor, double mini, tramp, from height).
Generally for the rest of us, it's 1-2kg ankle weights whilst doing calf raises or leg lifts. We will sometimes use 5kg weights for specific lunges, tricep dips, or a few other things. 2kg, depending on number of reps.
I do remember in gym though using 2kg weights for dorsel lifts etc.
I'd rather have my athletes use resistance/theraband etc and partner work - there are lots of really effective exercises out there. Body weight is effective, and it is important to train the muscles in the way you want to use them (i.e. lots of plyometrics, developing strength through skill repetition).