Paper from the 1800's is often quite acidic and so , with heat and humidity, will begin to degrade, become yellow and brittle. You can slow this down by keeping documents cool and dry and out of the sun, but often when you notice it the process is pretty far gone. Paper conservators can stabilize and strengthen valuable paper documents, but it can be ruinously expensive to conserve everything...especially if there are 100's of letters that only say mundane things, like the weather is fine today but Mother's rheumatism still pains her.

But most of the time you can handle them briefly. You can open the envelope ( even gently cut it open with a sharp knife) , read the letter, and then scan it and the envelope. You can then store them both flat, between sheets of non-acid paper. You can open the envelope flatter for storage as well ( who cares if it gets torn a little?) And you can make sure that the envelope and the leaves of the letter have a date, or a common mark .something that they can share in case the leaves are separated. Stored flat, all these could all go into an acid-free box, then the boxes go back into those tubs- and into a cool, dry place.

That's a lot of letters, so you'd want to pace yourself, give yourself a weekly goal. It can be very hard to intelligently evaluate a big dump of information, and some of these letters are going to be much more important than others. And, from what I have seen of family letters, many, many of them will be very unimportant. (Because, often what they are saying is, I'm fine, how are you? In days of high mortality and workplace risk, that was all that was needed to be transmitted.) If you do have something special, you can consider it for conservation. A local museum can usually put you in touch with a paper conservator or, failing that, a larger public library.

Unless you've got valuable autographs, famous authors, the most valuable part of these letters is their information. Sitting piled in those tubs, that information is inaccessible, almost lost. By scanning it, digitizing it, you're making it accessible. That's a good thing.