It's easy to go light and cheap at the same time and don't let anyone tell you different:
Shelter: 4 mil plastic 8x10, $2, wt., maybe 8 oz. for tarp.... Use a 3X8 for groundsheet - or use 3 mil for the gs.
Line (for shelter and other things): mason's line, maybe $4 for 500 feet..wt. 1/4 oz for 50 feet.
cooking: grease pot - under $10 wt.5oz.... alcohol stove from pop can, free, 1/4 oz to 1 oz., depending..... fuel, denatured alcohol, $4/quart.........fuel bottle, small disposable water bottle, free, 0.7 oz..... Spoon, disposable fast food spoon........Cup, Ziploc 1-cup semi rigid container - $4 for 3, wt. 0.4 oz.

water bottles: plastic pop bottles, free, 1 oz. max

sleeping bag: any reasonably light, all nylon covered synthetic bag from discount store. Best bet: semi rectantular bag cut down without the zippers to make a quilt -- $25-30, wt after modification under 2 pounds (a good target weight) Sometimes you can find very light quilts or comforters for home use that will make good backpacking quilts. I had one once that weighed 1.5 lb.when tapered.

sleeping pad: cheap blue foam from discound store or foam/foil windshield sun screen.

backpack: large day pack or book bag - used. These usually run around 2 lbs. and will hold everything except maybe the pad. Add lash points.

GoodWill, Sally and other such stores are good places to lurk for gear.

Get the idea?