Here's what I'm including in my book about the history of blogging. If anyone knows anything different, let me know!
Many sources agree that the term "weblog" was first used in December 1997 by Jorn Barger (www.robotwisdom.com/) when he used "weblog" to refer to a web page containing a list or "log" with links to other web pages that the "weblogger" found interesting. Barger is often credited with creating one of the first weblogs. In early 1999, credit for shortening "weblog" into "blog" went to Peter Merholz (www.peterme.com) when he began referring to "blog" on his own weblog.