I was wondering if there is a formula for how much weight a person should limit themselves to when carrying a pack?

My wife has had trouble carrying the weight I put in her pack. On a short hike at the local state park I placed as little weight in her pack as possible. Then we hiked out and we camped for a night. The next day while hiking out she complained about her hips bothering her.

I'm not sure if it's simply her age catching up, lack of being in decent physical shape or too much weight.

I think I had her carry about 15 pounds maybe 20 but I would have to really weigh the gear.

Theoretically, 20-25% for scouts backpacking according to this great article. But that is just a rough guideline since it is dependent upon so many variables, and portaging rather than backpacking adds even more variables.

How far are you hiking with the pack, how strong is she, how good is the pack at distributing weight comfortably, how heavy is it, etc.? The hips may not even have been as related to the pack weight as to hills, sleeping on the ground, distribution of the weight, etc.

In my wife's case, due to a neck/shoulder injury, she can carry her sleeping bag and clothes and that's about it. And not for very long.

If I had to guess about your wife, I'd suspect a combination of everything you asked. Too much weight for someone of her physical abilities/condition. Age you can't do anything about, but you can lessen the weight, and if she enjoys it she can work at building strength and conditioning.

I've reached the age where I realize that if I want to continue doing the things I want to do, I need to put some effort into staying in condition. I suspect that 10 years from now, I'll have to work even harder at it, just to maintain less ability.

I think this has to do more with general conditioning and not the weight. How many miles per week do both of you walk and how long have you been doing it? When I was younger I carried 25% of my weight for 5 days without feeling any pains. That was with a couple of months of intense training.
Do you do day hikes or walks every night after work? Walking becomes more pleasurable with frequency.

I was always taught that 1/3 your body weight was the maximum you could safely carry, and having broken that rule can confirm that doing so is a bad idea. 1/4 your weight is probably the limit for comfort.

I don't think any formula works, because we are all different in age, strength, fortitude, comfort level, etc. etc. I think it works best all around not to dwell on how much we should be able to carry, and just work on lightening our loads as much as reasonably possible. Doing this has had a huge impact in the shear enjoyment for me when backpacking. I can hike further, faster, and feel better at the end of each day. But that's just my approach, it may not be for everyone.

In your case, though, I would think that if you want the hiking to be enjoyable, you may simply need to carry a bit more of the share so that your wife will be able to enjoy the experience with you. So I still think that it doesn't come down to formulas, just what you need to do to be able to continue hiking together.