Many magazines at one time were the size of a ‘B’ (11 x 17") size sheet of paper, it would seem, the way Life was until the late nineties. Of course, Life was a straggler for many years, I know—about when did magazines shrink to the ‘A’ (9 x 12" -ish) size they are today?
Could it be because people more and more would read them while traveling?
Many old magazines have always been 8.5 x 11 (Time, New Yorker, National Geographic, etc.). I think it was mainly the pictorial magazines such as Life, Look, and the Saturday Evening Post that were over-sized. There are still oversized mags (Rolling Stone, Spin)
Continuously over the past 10 years or so, because paper costs are getting so high. I worked at a normal (letter) sized magazine, and we trimmed down by about a quarter of an inch, thereby saving millions of dollars a year! Not too many big magazines left, because the profit ain’t there. Just like there aren’t too many magazines left with giant staffs, or expense accounts for writers. 
What toadspittle – it’s all about the cost of the paper. We put out a lot of titles, and went through a real PITA period about two years ago when we had to redo everything because the trim sizes went down 1/4".
Shutterbug used to be tabloid (or close to it) sized. But, it had a huge (I mean MASSIVE) classified section. Then, the explosion of the internet, with all it’s eBay type places, virtually nullified any reason to maintain a large want ad section for all things photographic. So, it resized and reorginised. Yeah, I miss the old ‘feel’ but it’s still one of the best photography magazines around.
Of course, that is just one example out of many, so it barely fits the OP’s general question.
It’s only partially about the paper. It’s mostly about the advertising.
Magazines exist for only one real reason: to give advertisers a place to get their ads seen. When advertising drops the value of the content of the magazine doesn’t matter. The magazine still goes out of business.
Advertisers hated having to produce two different sizes of full-page ads, one for the standard-size magazines and one for the larger-size ones. They put huge amounts of pressure on those magazines to standardize.
Since it’s also cheaper to use less paper and it’s easier and cheaper to find presses that can do the work, the business side of the magazine found this a win-win.
The big push on this was probably 30 years ago, so this trend started way before there was any thought of the internet.
As I noted in my post, my example was specific to the one mgazine noted and not meant as a general rule.
It’s also about postage. At least in the 1970s, when the downsizing began, it was cheaper to mail a smaller magazine with more pages than a bigger magazine with fewer pages. Added to the other factors mentioned, it became an inevitability.
I believe Rolling Stone has shrunk over the years. Just not down to letter-size.