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The classic advice given to backpackers trying to limit the weight they have to carry is “Pay attention to the ounces, and the pounds take care of themselves.”
Brooks Landon M.A. Ph.D.. Building Great Sentences: How to Write the Kinds of Sentences You Love to Read (Great Courses) (2013).
How's the quoted sentence true in reference to backpacking specifically?
The pounds cause most of the mass and physical burden.
There are several expressions akin to
Pay attention to the ounces, and the pounds take care of themselves.
The most famous saying is
Take care of the pennies and the pounds will take care of themselves.
ascribed to Lord Chesterfield in 1747 by Phrase Finder. (There were 240 pence (pennies) to the pound sterling.) The statement means "to be thrifty and not to squander money", and was memorably updated by Sen. Everett Dirksen, commenting on how federal spending tended to get out of control:
a billion dollars here, a billion dollars there, and pretty soon you are talking about real money.
Ounces or pennies or a mere billion dollars, the principle is the same: look at the cost or weight of every item you buy or take with you on a backpacking trip and try to pare down the weight or cost and your wallet will be fatter and your pack lighter.
Some backpackers (and racing sailors) cut the handle of their toothbrush in half to save weight, but you don't have to be that extreme. Some mountaineers make one of their water bottles do double duty as their pee bottle when they are tentbound, but IMO, that is going much too far. Carry extra clothes so you can change into dry clothes, but don't worry about dirty clothes. Repackage food to eliminate glass and cardboard. Take a tiny travel sized tube of toothpaste (preferably already partially used) -- or no toothpaste at all, just floss -- your teeth won't drop out in a couple of weeks.
Everything you take should be essential, according to your standards, and everything should be scrutinized: (1) do I really need X? (2) do I really need this much of X? (3) Can I repackage X to eliminate weight?
It does make sense to watch the weight of your gear and go for lighter gear when possible. A few ounces here and there will add up to pounds.
On the other hand, it is also possible to be penny wise and pound foolish and in my experience at least, this is far more common, you will see overweight hikers and climbers buying titanium gear for example.
I once had another backpacker with his gut hanging over his belt inform me that his water shoes were 4 ounces lighter than mine.
Realistically, this is just a saying and not an ironclad rule.
Little things add up.
There's lots of lists of this sort of stuff. Some people are fanatic about it. I heard of one guy who took the extra 4" off his boot laces. Another who cut out the liner of his running shorts.
It can go too far. Another guy used a cheap $2 use once special rain jacket. And it rained the whole week. Fortunately for him, I had a small roll of duct tape.
Generalization: For longer trips you need better gear. Sometimes better=lighter. Usually better=tougher.
Keep in mind how long you are going to be miserable if something doesn't work. I bring 2nd pair of footwear with me. Twice I've had to loan my 2nd pair to someone who brought the wrong footwear with him.
If we got normal weather, and I've worn everything in my pack, I figure I've cut it too fine. I should have 1 layer more than I expect to need. What do I do if someone in the party twists an ankle on a rainy windy pass, and we are moving at 1/3 speed the rest of the day.
You can cheap out for low probability events if you have a way to endure it. E.g. I might not bring my rain gear for a trip in Canyonlands, but resign myself to waiting it out huddled under my tent fly.
My repair kit has more stuff in it for a large group than for a small group. Peel and stick mosquito netting to fix holes in tent netting. 1 each of every type of buckle on every pack. (Doing a week with a broken waist buckle isn't fun) A sewing awl. A weekend trip, I won't bother with the roll of duct tape. For a 3 week canoe trip, I brought 5 small rolls of duct tape. Group was 25 kids and 5 adults. (Voyageur canoes) Every paddle, bailer, pack, gear had a stripe of coloured tape on it. Made sorting out the gear at portages infinitely easier.
My first aid kit is somewhat group-size dependent, but more trip-length dependent. I carry enough anti-biotics (broad spectrum ampicillin and check if anyone in your group has allergies) to treat one individual for the length of the trip. Burn dressings for 1 individual for the trip, or to next resupply point.
You find that 'expedition grade' stuff is a lot less fragile, and often somewhat heavier that the super light stuff.
The less you carry, the lighter your load, but also you are less capable of dealing with the unexpected.
"Take care of the pennies then the pounds (British money) will take care of themselves."
but also
"Some are penny-wise but pound-foolish."
