Let's talk about the size issue first:
PDF is a pretty complex file format (the specification is almost 1000 pages long), so there is a lot of "stuff" happening in your PDF file that the user is normally not aware of. One of these things is how resources are used: It's possible for a number of pages to share the same resource, so that it only has to be embedded one. The best example for this is a font: If you use the font "MySpecialFont" on every page in your document, it will only be embedded once (that is, if you've used a good PDF generator). When you now split that document into documents that only contain one page each, that font needs to be embedded in each of these one-page documents. That's why the sum of the size of the resulting documents is larger than the size of the original document. This does not just apply to fonts - when you use e.g. watermark or background images, the same thing will happen, and there are other instances when resources are shared as well.
As far as the underlines go, that depends on how the underline was created in the first place: Most times, an underline is really just a line under the text that has nothing to do with the actual text. In that instance you will have to select the line and delete it. If the underline was added in a way so that Acrobat "knows" that it belongs to the text (e.g. because you've used the underline feature in Acrobat), you will be able to just deselect the underline button and it will be removed.
Thank you Karl--always appreciate your knowledge!