In my humble opinion, it's better to have one big file.
(a) As Amadeus notes, if you have to search for something it's easier with one big file. Checking continuity is one example, but I routinely do all sorts of searches in my work-in-progress. "Didn't I mention X before?" "Oh, I just thought of something I need to add to the discussion of X." "My friend who did some proof-reading for me said there's a mistake in the discussion of X." Etc. I MIGHT remember which chapter something is in. But I might not. And why waste brain cells remembering exactly what's in each chapter when the computer will do that for me?
(b) It's easier to move things around. I often say, Oh, wait, I originally planned to explain this in chapter 10 but something in chapter 5 is dependent on that, I'd better move it from chapter 10 to chapter 5.
(c) You say you're using Word. Word can automatically build tables of contents, lists of illustrations, etc. But that requires everything to be in one file.
(d) It's just easier to move back and forth. If you assign a heading style to your chapter titles, Word will give you a list of chapters in the left bar. Then if you're working on chapter 4 and remember something you want to look at or change in chapter 3, you just click on "chapter 3". With separate files. You'd have to open another instance of Word, find the other file, and load it. Okay, that doesn't take hours, and if you do it once a week maybe no big deal. But I often find myself going back and forth constantly.
I'm hard pressed to think of an advantage to having many small files. Twenty years ago when you had to fit a file on a floppy, and when it might take a long time to read a file, I'd break up documents like that. But not today.