I don't think weight is as much of an issue as geometry and fit.
My littl'uns all did the gentle graduation from 16", through 20" to 24" kid's bike.
The 16" and 20" were heavy, but the geometry and build quality were good in both cases. The 16" had one gear, the 20" five. All three kids rode both in succession.
They all then went through 24" bikes (all up to this size were MTB look-alike machines). The 24" bikes were aluminium-framed (I had two because the kids were close in age). Despite being aluminium, they were still heavy-ish. This was simply not a problem. Weight is an issue really only when climbing. All the children loved to climb in the Malvern Hills (and loved to descend even more). No issue with weight. My kids were not mini-Pantanis, just kids on bikes.
What was important to me was that the quality was good, the components were good and the geometry made riding a pleasure. I think the weight of children's bikes can be high, but it is not an issue to get one's knickers in a twist over.
All our kids were doing fair mileages on these clunky MTB-type machines (70 miles to their grandmother through hilly Wales) from the ages of 8, 9 or 10. They had nothing to compare the bikes to, so the weight was not an issue. There were one or two moans about saddles, which were addressed.
Now much older, they all ride good, lightweight Italian road bikes and love them. None of them has ever made a single negative comment about the weight of the smaller, heavier bikes they rode as kids.
I hear similar moans about the reach to levers on kid's bikes. As long as there's some adjustment, you can usually find a safe fit.
All my kids' bikes were bought from my LBS. It's a place I trust and the quality is good. None were 'known' brands.
If there was a sizeable market for built-to-a-weight kids' bikes, someone would be meeting the demand with volume machines. Realistically, there is not. Even parents who are keen on cycling (as I am) have more to think about than shaving a few kilos off a kid's bike.
