I have lost about 50lbs since I started cycling. The combination of weight loss and increased fitness from riding have been showing in my ride speed.
Sunday, I did an 11 mile training run on the '83 World Tourist with an average moving speed of 16.93mph. That is the best speed I have ever clocked (I count time from when I leave the driveway to when I stop at the front steps.)
Today, I did my 21.3 mile commute in 1h28+m with an average speed of 14.5 mph! That is awesome for me

My first commute was about 12.5mph.
Therefore, my conclusion is that weight loss + increased fitness = faster average times.