The fact is, there are practical limits to what you can carry. But even after taking into consideration weight, space, and restrictions on certain morphine-based painkillers, you still can carry plenty that will help your trip be more comfortable, while giving you some assurance you can take care of major problems.
First, consider the first-aid scenarios. They're really fourfold. First are minor problems such as cuts, scratches and blisters. Those are pretty easily dealt with through a selection of adhesive bandages, an antiseptic liquid such as Betadine (dispense from big bottle into smaller screw-top plastic container for packing), and over-the-counter antibiotic creams. For slightly more serious cuts, adhesive tape and several sizes of gauze pads are useful. Pack as well a mix of over-the-counter painkillers Tylenol (acetaminophen) and Advil (ibuprofen) taken together, for instance, approaches some prescription meds in effectiveness.
Number two would be biting insects and rash causing weeds. Cortisone cream handles the former. If you're in poison ivy/oak territory, pack along some IvyBlock lotion for preventive steps, along with some soap to cleanse the area and perhaps an oral antihistamine such as Benadryl.
Scenario three includes severe cuts or lacerations. These are actually pretty common I've seen people slip and bang their arm on a sharp boulder, cutting the triceps down to the bone, or fall on an ice axe. For injuries such as that, add some big gauze pads (commonly called "battle dressings") or some absorbent sanitary napkins.
Last on the list is fractures. These are hard to effectively pack for. I always carry a big triangular bandage (also good for #3) that can be used to tie a splint or can be used as a sling. Stuff you already have is handy here a rolled-up sleeping pad makes a fine splint in conjunction with a straight stick or a trekking pole. You also can purchase ready-made splints, such as the flexible, aluminum-and-foam SAM splint ($15 for 4"X36" splint).
All this should fit well into a bag that's no bigger than a hardbound book, and weighs about the same. I make my own kits, but of course you can buy a ready-made one. A good choice: The Adventure Medical Weekender ($52).
The last thing, however, doesn't fit in any pack: It's knowledge about how to apply first aid, and the willingness to use that knowledge. A lot of stuff turns out to be intuitive pressure to stop bleeding, immobilize a fracture, things like that. But you really want to take a good first-aid course, then tell yourself that your knowledge and your common sense will serve you well should the need arise. And when it does, step in and take action. Someone's life may depend on it.