Most of the stuff you have looks good. If you like to go backpacking, just go. There is nothing that will constitute a major problem. Depending on the exact area, you may need less or more water. I usually carry two 20oz bottles of water into the ADK's. You can go lighter as wanted.
Like you say and others have commented on, the bag would be the first item to replace. And it will likely cost as much as the rest of the gear combined. You can make one. A good quilt can usually be made for about 1/2 the cost of purchasing a good bag. Check and/or post to the MYOG section for help there. Same for a bivvy.
The tarp you have is a good one.
Canisters are generally less efficient than most people think. The general cost for carrying fuel should include the fuel bottle. Soo, 8oz of fuel with a 5oz can adds up to 13oz. For the first 4 days out, this is OK, but you could do better. A home made Caldera cone, for example. The complete cooking system will be the entire weight of what you use: fuel, bottle, stove, pot, cup, spoon, lighter, windscreen. By anylizing everything needed for one, two, three or more days out, you will find you can indeed do a better. Both the starting weight and ending weight should be averaged, of course. 'Corse it is hard to apply a number to things like simmering. Alcohol stoves typically do not simmer well.
First aid? Well, as they say, what you know doesn't weigh anything. Get and read a couple books (they will likely differ in details.) Then figure out what you actually need. For example:
You cut your finger. You need a clean bandaid. You need to clean off your hands to work. You need to clean off the wound, removing any debris. It needs to be fairly sturdy so you are not constantly fussing with it. I would wash with a little clean water. Then with a little fuel wash my hands down. Sterilize the wound with alcohol. With a strip torn from my bandana, I would dose that with alcohol. Then cover the wound. Then with a strip of duct tape wrap it around the cloth bandage to reinforce it and keep it clean. Should last a couple three days with no problems. In fact, I have had these on for a week with no problems.
The point is, I did NOT carry anything extra. I *knew* how to keep it from getting infected and making me sick. It was an outdoor bandage, not too pretty.
You may need Tylenol PM or Advil. Mostly, First Aid is knowledge and not things. You can improvise most splints, cold and hot packs. If you get hurt bad enough that you need to get out, you should be prepared for a painfull, carefull trip out. In almost every case, *you* will be the one performing the rescue. Not to worry, this is RARE.