Acrobat is different than e.g. MS Word or InDesign when it comes to saving: There are two different ways of saving a file. To understand why, let's take a step back: Let's imagine you have a 1GB large PDF file, and before you go to print, you need to fix one typo. You open the file, replace one character and then save the file. Saving a 1GB large file will take a while, and you sit there and wait and wait and wait. Because of that, Adobe created a way to only save incremental updates, in which only those elements that are new or were changed in a PDF file are appended to the original PDF file. So, instead of writing out 1GB of data, you only write a couple hundred bytes that are getting attached to the original file (which is already on your disk, and does not have to be rewritten again). This takes a split second and you can go on to your next task. This is what happens when you select "File>Save" (or Ctrl-S/Cmd-S) in Acrobat.
A "Save As" does something different: It will recreate the whole PDF file from scratch by taking the original file and all incremental updates that are in the file and throws out anything in the old file that is no longer needed. If you have a 100 page document and remove 99 pages and just do a Save, the file will actually be a little bigger than the original file, once you do a Save As, you end up with only the one remaining page in the file.
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