What causes PDF file size to increase when saving in Preview?
In his little-known novel, PDF Karenina, Leo Tolstoy wrote,


  Optimally encoded PDF files are all alike; every sub-optimally encoded PDF file  is sub-optimally encoded in its own way. 


It's hard for anyone to answer why your PDF files are larger after Preview modifies them. A PDF file consists of many different kinds of data: images, content streams, fonts, document overhead, color spaces, extended graphics states, and a cross reference table. Just like one sentence might be concise and another verbose, but both are valid English and say the same thing, so too one PDF file might have a more verbose way of representing the same content as a more concise PDF file. We'd have to look at your exact PDF files. It's likely that they were created by a variety of different pieces of software, some consise, some less so. 

It also matters what version of Mac OS X and Preview you are using, because that determine the software that writes the new PDF file when you do a Save As in Preview. 

I can, however, tell you what gets larger about some of my PDF files. This story applies to my computer, running Mac OS X 10.5.8 and Apple Preview 4.2 (469.5).

One file, Giulio.pdf, is a 22-page document with text as text, not scanned images. It is 461,092 bytes large. I opened it in Preview, did File... Save As..., and saved it under a new file name. The new file is 724,421 bytes, or 57% larger. 

I opened each file with Adobe Acrobat Professional, version 8.3.1 for Mac OS. I did Advanced... PDF Optimizer... Audit Space Usage.... A small dialog box gave a break-down of how many bytes were due to each category of usage, plus the percent of the total file size for the category. 

The original Giulio.pdf has 390,754 bytes (84.75%) devoted to content streams, and zero bytes devoted to images. It is in the PDF 1.4 format. The file saved by Preview has 675,846 bytes (93.29%) devoted to content streams, also zero bytes of images, and is in the PDF 1.3 format.  Preview made the content streams 285,092 bytes larger, and that represents 73% of the file size difference between the two.

I wondered if the PDF 1.3 file format was inherently less efficient for storing this kind of file. I opened the original Giulio.pdf in Adobe Acrobat Professional 8, and did Advanced... PDF Optimizer... Make compatible with: Acrobat 3.0 and later and pressed OK. I saved the resulting file under a new name. The resulting file is in the PDF 1.3 format, and was 452,356 bytes, or smaller than the original. Its content streams are 375,171 bytes (82.94%), a similar proportion, but smaller than the content streams of original file.

Thus it seems we can conclude that the Preview app on Mac OS X 10.5.8 is not as efficient as some other PDF creators at making concise content streams in PDF files, and the difference is enough to account for three-quarters of the size difference in a PDF file without images.

I did a similar experiment on form k.pdf, a 1-page document scanned from paper. The original file is 303,730 bytes, of which 298,197 bytes (98.18%) are images. A copy of this file created by Preview using Save As... is 300,601 bytes, or 1% smaller. This file size difference is more than accounted for by a smaller "document overhead" category of bytes in the file created by Preview.

Thus it seems we also can conclude that Preview doesn't always cause a PDF file to increase in size. It depends on the nature of the original PDF file, and how concise it was to start with.