I am a decent climber and a better scientist, and I strongly suspect there is no scientific answer to your question.
I have been on my long climbs and backpacking trips where I had to carry a pack.
The most important factor in how much weight
I (or my friends) carried was not height, weight, or gender, it was fitness.
Your strength, endurance, and your experience carrying weight will determine how much weight you can carry comfortably.
I know this is probably not what you wanted, but I believe it is correct.
outdoors.stackexchange.com/users/767/theJollySin
It is not your weight that is limiting your ability to carry heavy backpacks, it is your strength.
You should determine your backpack weight based on strength and what you've previously carried, not your bodyweight.
outdoors.stackexchange.com/users/None/
I used to apply the 30% rule, and for out of shape adults it works pretty well.
But I worked with teenage males, ranging from the 70 lb dripping wet grade 7 to the 160 lb lean as a rake grade 12 just starting to come into his adult strength.
But in between were a bunch of butter balls.
They were already carrying excess weight.
Those older boys (which we shamelessly used as pack mules on trips with the younger ones) would quite easily carry 80 lb packs.
And Ive heard of climbers doing the same on journeys to base camp.
Those 70 lb grade 7's didn't have much trouble with a 30-35 lb pack either.
So the rule I came up with was 50% of lean body mass.
In practice we took an eyeball look and categoried like this: Visible ribs.
50%Can see muscles, but not bones.
40%Layer of baby fat
30%Obvious Molson Muscles overhanging belt line:
25% Small plump kids could barely carry their own clothes and gear.
We made a point of finding something bulky but not massive so they would still feel like they were contributing to the group.
Egg noodles and scalloped potatoes.
Once on the trip, we sometimes had to shift things around.
The goal was to equalize the discomfort.
This estimation rule usually meant we only had a couple of individuals whose load we had to lighten.
You can train yourself to carry heavier loads.
When I was in university, I borrowed a couple of lead bricks (35 lbs each) and kept them in the bottom of my book bag.
Had to restich the bag every few months -- they aren't designed for that kind of weight.
I lived a mile from campus, and biked or walked to class.
(Warning: Biking with a pack that heavy is very odd)
The key is that you develop habits of posture that minimizes the pain.
While daily work this way is best, setting up a pack at 40% and carrying it for an hour or so at a time on walks in the park.
(wear the shoes you will on the hike too.)
will help, either by training you to the higher weight, or by motivating you to leave stuff at home.
outdoors.stackexchange.com/users/2157/Sherwood Botsford
Though there is no scientific answer, you can make use of some experience-based guidelines.
They vary much and none is "true".
There are some of our local considerations: Our club's empirical threshold is 30% of you body weight.
Which simply means, that if your pack is heavier than that
and you don't have much experience, you should strongly consider either removing some unnecessary items or choosing a shorter trip (so you can carry less food).
Of course this varies wildly and body weight is just one of the variables, along with strengths/fitness/endurance, skll, motivation, age, sex (girls are stronger in %), backpack quality, ...
In our trips you sometimes have to carry food for about 2 weeks (and all the technical and camping gear), so this 30% guideline is somtimes violated.
And our fathers, when things were much heavier, used to carry as much as 50% of their weight.
And sherpas routinely carry up to 100%.
Backpacks do damage you health, if they are more then your personal limit.
So it's wise to increase it slowly (starting from shorter/easier trips).
Note, that heavy backpack needs some skill to put it on right, otherwise you can damage your back before even walking out of the door.
Regardless of the limits, if you can make you pack lighter without jeopardizing safety, do it.
Poetically, if you pack is 100 g heavier than your friend's, after you come to a camp after a day hike he starts to relax and you first have to run with a 10 kg bucket of water for 5 minutes.
To sum up, I wouldn't recommend having >30% on your first mountaineering trip, but you shouldn't constrain yourself within any particular "theoretical" limit.
If you want to stay healthy, listen to your body.
outdoors.stackexchange.com/users/1794/Steed
Your backpack weight should be 20% of your body weight, and get a 30-40 litres backpack.
The backpack should fit nicely on your back with it resting slightly above your butt, and it should not obstruct your head movement.
Backpack weight distribution is 40% on shoulder strap and 60% on your hip strap.
outdoors.stackexchange.com/users/2061/Hachi28
I am eager to go mountain climbing but cannot carry heavy backpacks because of my light weight. I want to know if there is any scientific equation to help me know how much weight is safe for me to have on my back.
What is scientific relation between body weight and backpack weight in mountain climbing?
outdoors.stackexchange.com
<climbing>
outdoors.stackexchange.com/questions/3656
outdoors.stackexchange.com/users/2059/Persian Cat
Some clubs recommend that the weight of the backpack should not exceed 30% of your body weight. Other people recommend 20%. Backpack weight should be distributed between 40% on the shoulder strap and 60% on the hip strap. Others say that your strength, endurance, and your experience carrying weight will determine how much weight you can carry comfortably.  This varies wildly and body weight is just one of the variables, along with strength/fitness/endurance, skill, motivation, age, sex (girls are stronger in %), backpack quality, etc. You should determine your backpack weight based on strength and what you've previously carried, not your bodyweight. It largely depends on your strength, fitness and experience, though 30% of your body weight is a good rule.
30% of your body weight is a good rule, with 40/60 distribution between shoulder and hip straps. Strength is the key factor, as well as fitness and experience.