I cannot emphasize any more on how integral unit tests are for the success of an application. Recently, I was working on a small demo application using test driven development. I had to change the design of the application number of times to accommodate the new features and changes. My only shield against these changes was the unit tests that I wrote. After performing the changes I got few broken tests. That was good! Because now I know what is broken and I can go and fix it.
Unit testing does increase the code (testing code) but the advantages are far superior that will help you in the long run.