Webmatrix is running on your local machine with it's own built-in Web server and I presume is accessing a local MySQL server that's on your local machine. If that's the case the only way to share this with a colleague is to upload the complete file structure to Dropbox and a backup of your MySQL database, have the person download the site and database backup and set both up on his local machine. He would need to be have already created a BLANK MySQL database on his local machine with the same username and password as on yours (most people set up Local MySQL with the User: root and your on password).
This is actually a lot of work and a real hassle to do each time if you are making constant changes that you want to share. Might be much better to get a cheap hosting account and give the person access. Or you could look at a Free Windows Azure Website account.