A quick disclaimer for the long post: I'm a bike mechanic…
Here is what I personally bring on pretty much all bike rides, regardless of length or locale:
-two tubes; 26" because your can use them on any size wheel and they pack smaller and lighter
-patch kit; because there is no doubt you'll get one more flat than you have tubes to deal with
-two dollar bills; work great as tire boots and as…money
-curved sewing needle and 3-5 ft of waxed floss; use to repair any bags that blow or large tire gashes
-tire pump; get a small one, specialized, blackburn, and pro make smaller ones
-suspension pump; ignore for your purposes
-spare spokes; x2 and if you've got the right set of wheels, you can make the same length work for each wheel and side; if you've got a freehub on the rear that can't be pulled of with the entire cassette (dt swiss, joytech style, etc.) you might plan on having a 'fiber fix' spoke
-3-4 heavy duty zip ties
-allen/torx keys for all bolts; for me personally it's limited to a 4,5,10mm allen and a t10 and t25 torx; definitely figure out what you need and don't take things that you don't
-Leatherman Squirt PS4; has one or two things I don't need (scissors, file), but has screwdrivers for derailleur and other adjustments, and pliers for any nut heads and/or nipples
-chain tool
-spare chain links and master link
-spare cleat bolts; ignore for your case
-spare bolts in appropriate lengths for various parts of the bike; I personally take bolts to replace any bolt on the seatpost and collar and a stem bolt. Figure out what you might need for yours. Do note it's waaaaaay easy to got overboard on this one. Just figure out the common things that could break and ask yourself if you could ride in reasonable comfort and safety without that bolt. For things that have multiple redundant-ish bolts (chainrings, 4-bolt stem plates, disc rotors), don't worry about an extra, for others, use your judgement.
-spare derailleur hanger; don't forget bolts if applicable
I think that is it. A great way to minimize the bulk and weight of the kit is to either take apart a multitool or buy individual tools (allens, torx, etc.) only in the sizes you need. The only 'full-size' tool I have is a 4mm allen wrench. I use it as the handle for all the other sizes that were pulled out of a disassembled multitool. It sounds like a pain in the ass, but if your bike is dialed and you don't always have to work on the bike on the trail, it's good. To put a little context into the size and weight that you can get to; I fit all the above except the tire pump and spare spokes into an Arundel Dual seatbag. Everything fits in, it all stays on the bike, and I never have to worry about forgetting something.
Of course, as with everything ultralight, or really just anytime you're away from civilization: the more knowledge you have, the less you can bring. A good bicycle repair book, and the knowledge from it, will go a long way towards getting you back to civilization via bike instead of on your feet with a bike on your back.