My humble answer: Great Question. The answer is a definite yes. In fact, I actually have my own experience with weight loss as I wrote about in this post and also in this post. I'm the same height as you, and was up to 220 pounds, winded all day, and my asthma was poorly controlled. After dropping 40 pounds I felt like a new man, and my asthma was better than ever. When I stop eating right and exercising, and my weight creeps back up, my asthma gets progressively worse. So in that sense I've learned exercise and eating right is not an option for us asthmatics -- it's mandatory.
So, just based on my own personal experience, I'd have to say the answer to your question is YES!!!
Speaking of studies... and not that we asthmatics need to do a study to figure this out... Many studies have also linked obesity with worsening asthma control. I actually have an upcoming post about these studies, but in the meantime you can click here for more reading about the asthma/ obesity link. Or you can google it.
I hope this answers your question. If you have further questions, or need some tips how to lose weight with asthma, let me know. Rick.