The big 4 are
Weight is what it is on these, based off of your budget. When you go into the Ultra Light territory, you really do sacrifice longevity/durability, despite what distance hikers will tell you.
Aside from the big 4, Re-assess what emergency supplies you are likely bringing.
>How big is your First Aid Kit?
Chances are its got too much in it
>Do you have patch kits for your tent, sleeping pad, etc?
You're not going to need a permanent solution on the trail. Repair it at home, and bring some duct tape wrapped around a bic lighter. it will do the job until you can get home to repair.
>Bringing emergency bankets, or other emergency shelter
Don't do this, you have a tent and sleeping bag, which is better than anything else.
>Deck of cards or books
You're bringing a phone, load all that shit onto there.
>Processing fire wood
This is all up to preference. Realistically you don't need an ax and a saw. But if you want to practice your skills, its up to you to decide the weight/benefit ratio. To be honest, in the many trips I've been on, I've realized you dont need either. If you get the fire started, you can make it hot enough to burn a stick straight out of a lake (I've actually done this) You can get any size log, and just feed it into the fire as well. This is a good area to both "challenge" yourself, and save on weight if you feel comfortable.
should be minimal. Include a straw, the rubber straw from a sawyer mini works great as a fire blower
Really depends on what type of trip you're doing. If it's a base camp type of trip, and there's always going to be a fire, maybe bring one can of fuel between all campers.
Lastly, I recommend sharing gear with your group/partner. You really only need 1 first aid kit, ax, saw, and if it's big enough, only one pot to cook/boil water.
I'd love to see your kit, and I'm sure many are eager to give their oppinion.