Bottom line: a commute that short has to be ridden really hard in order to get into a zone where you're really burning calories and will continue to do so after the ride is over. I don't like to arrive at work in that condition, so I chill on the way there... mostly. There are points on the ride that are too much fun and I can't help but bomb my way through them, but I try to look unbothered when I arrive.
I freakin kill it on the way home. At least sometimes, you need to get nearly deliriously burnt on the bike to get real work in. Bikes are efficient; they make miles really easy. You want quick work? Try jogging. I can't, breaks my feet and knees, and I hate it besides.
Six weeks is a short time, but I do think you'd be seeing more of a difference if you were absolutely murdering your workout a few times a week.
Commuting to work is one thing, fat-burning is another. HTFU and start kicking some arse.