I don't have an answer to your weight loss question, though I suspect you would probably lose some volume in your cups, but its hard to say how much.
I wonder if you have had a really good bra fitting lately? I ask for two reasons, number one, you mention that your chest is the first thing you think people notice about you. I've always found that a properly-fitting bra can totally change your appearance by keeping your breasts up where they should be and keeping them within your frame. I wear a 36H, so I understand this can be a problem :)
Also, you said you wear a 38DD now, and that seems to be a size that is at or near the top of sizes that are readily available at most stores, so when you go looking for a bra, its what you end up with, because it's as close as you can get to something that fits and they don't carry anything else. I think A LOT of women who are wearing 38DDs would actually be much better off in a different size, but they don't know those sizes exist or don't know where to get them. I used to be one of those women. www.breakoutbras.com has great info on how to size yourself at home and get an accurate size. It's really easy. Or try Nordstrom if you live near one. I would stay out of Victoria's Secret, they aren't for those of us with large busts.
If losing weight is your goal then go for it, but a bra that really fits you might make a big difference in how you see yourself.
Good luck!