Yes, losing weight helped me get faster, definitely. In my early 40's, I lost weight, started running, and did a few races, halfs and a full marathon. I did the run/walk thing and I think my best 5K time was maybe 31 minutes or so. My best half marathon was 2:26. At the time, I weighed in the low 120's.
Then I fell off the wagon for about 2 years, regained it all (and more), and had to start over with the weight loss thing.

I couldn't even run at all when I started exercising again -- what a come-down after finishing a full marathon several years earlier!! As I lost weight and regained fitness, I started running again, and eventually found I didn't even need to do the run/walk thing any more. I'm a good 10 pounds lighter now than when I was running before and quite a bit faster. My 5K
PR is a little over 26 minutes and my half marathon
PR is 2:01. So yes, for me, that extra 10 pounds has made a significant difference.