To truly go super ultra light, you need to spend some dough. to just be lightweight, I'm convinced it's cheaper if you actually go through a basic semi light list that any kid could
use.

let's try - assuming above freezing type weather - weekender type trips.

alcohol stove (spend 30 minutes making one from discarded cans... ) $ 0.00
Wal mart grease pot or AGG pot $10.00
Plastic spoon 0.00
Pop bottle for alcohol 0.00
2x 1litre pop bottles for water 0.00
aquamira/pristine 15.00
4 garbage bags (stuff sacks, waterproofing, etc.) 0.00
Lighter 1.00
plastic cup 1.00
reasonable first aid kit $10.00
Pocket knife $5.00
headlamp (heck, Petzl E-light!) $25.00
Sleeping Bag or Quilt (I can buy an REI kilo flash 40 for $90 right now) $100.00
2 sets liner socks (poly) $15.00
2 sets merino wool hikers $25.00
blue foam pad $10.00
Good Set of Kids Running Shoes [2] They've already got them
Backpack (GG virga use blue pad for frame) $100.00
clothing[1] $25.00

[1] - i'm assuming like many kids. half their clothing is already synthetic. Find their favorite pair of athletic pants and send them with them. the $25 for clothing is to be spent at the thrift store or wal-mart rounding out what they don't have with synthetics. I'm gonna assume they take a set of long johns to sleep in, a fleece jacket, nylon windbreaker and a cheap light rain poncho such can be had at wal mart for a couple of bucks. easy to get at
the thrift store. long johns might have to be purchased.

[2] any kid will hike fine in their day to day runners. - yes you probably shouldn't take them boulder hopping down a talus slope in them, but get real - it'll work fine for starter hikes with quick drying socks.

There's a $340 start - if that' rich for your blood, substitute the $25 wal-mart snugpack style ripoff sleeping bag and put in an extra fleece to sleep in, and buy a walmart frameless ruck for $25, and you're down to $190. use poly dress socks and wool
socks from the thrift store and nock off another $35 so you are down to $155.

For shelter, lots of options. maybe a tarptent style beast, maybe shared with another
scout, or maybe a hennesey hammock, or six moon designs wild oasis - lets' say between $80 and $175 bucks. You can get more creative here to save money of course.

So that's $500 for the "cadilac" end with a hennesey and gear that'll last, or $235
for the cheaper stuff with 80 bucks toward a share of a shared shelter or he/she learns to tarp it. - if the troop has shared tents they may not need that.

What does the kid need to learn?
1) how to use the alky stove, and cook and eat FBC style.
2) How to use their shelter, whatever it is
3) how to hike in socks/clothes that can get moist, and put on dry ones to sleep in at night, change back next day when moving.
4) how to use aquamira/pristine for water.
5) How to put one foot in front of the other without excessive snivelling.

I mean come on folks. I see those kind of prices for just an overpriced heavy *backpack*,
nevermind what an Xbox and a couple of games costs.