Chose a readable font. Text files are shown with the browser default monospace font, but you change it to whatever you like best.
I think there is not much else you can do with raw text files in the browser. The next level would be to write in something like markdown and view the processed text, I think.
I suppose I could try to write something that scrapes the text file, adds <p> tags around paragraphs and presents it with some really basic CSS. I don't know how to code, but I might try cobbling something together.
Additionally, since it uses the Markdown syntax, it might give you more than paragraphs if you use more than line breaks. (Have a look at the quick reference for more about the syntax.)
Edit: Didn't see your answer to @kybernetikos. I still think this could help you out. Also note that in HTML (what you'll get by adding <p> tags to your text), whitespace is collapsed (except inside <pre> tags)
Instead of writing a converter yourself you could try to use Markdown on your files without modification and see how well it does. The design goal of Markdown is:
Markdown allows you to write using an easy-to-read,
easy-to-write plain text format, then convert it to
structurally valid XHTML (or HTML).