To add on, the last place to lose weight is your pack. Until you get everything ultralight, you need a fairly stout pack to carry it all in. There are lots of older non-hunting packs that can be had for a song (a quick search of my local Craigslist found an Arc 'tyrx Bora 80 for $100 and a vintage Mountainsmith -- similar to early Kifarus -- for $80 - there are many more options across the mountains in Denver) and will carry loads comfortably. Just make sure they fit you properly.
As mentioned, a tarp will really cut down on your shelter weight, but on the other hand they aren't necessarily the best gear to try your first time out. I'd look for a really light one to two man tent. REI has their Quarterdome on clearance now for what is a good price -- but it still may be out of your price range.
Check out an ultralight backpacking forum and you will get lots of cheap ways to cut weight on the non-hunting specific stuff. Not everything takes lots of money. Also, don't get starstruck by titanium. Much of the, much cheaper, aluminum gear is very close to the same weight. GSI Halulite comes to mind. Tent, sleeping bag, firearm, clothing and optics are where you will see the real pounds and ounces come off. I think archery gear is going to a bit more standardized in weight than rifle, but the same thought applies.
I found that the best investment I ever made was a digital postal scale combined with a spreadsheet. I weighed all my gear including what I carry and weigh (don't forget water, food, ammo/arrows, etc.). That really keeps me honest with what I pack. I throw in a lot less "just in case" stuff. I echo the suggestions to start truck camping, but you can combine that with just enough gear for an overnight if the hunt warrants it and/or you want to gain experience.
Good sources for bargain gear include Craigslist, some Goodwill stores, Sierra Trading Post, Steep and Cheap (be careful -- they had some long underwear I bought that was on clearance for $75 but available for $50 normal price from the manufacturer) and the REI Outlet or their garage sale (again be careful on pricing.)