Patience! It sounds as if your wrap is nice and tight while allowing you to eat everything, which is the best of both worlds. Bill is right...I also tend to get some food/liquid held back at the wrap site, but just take a few extra sips of water to get it through.
Also, if I chug water it tends to build up in my esophagus, then drain down. Less water at a time is better, but I am a big water drinker and in the habit of chugging a whole bottle down at once.
When I'm walking at a good pace on the treadmill I have to be careful because the water can splash up and get into my lungs a little, which gets me coughing. Because of that I pause my walking or slow down before taking a drink. It's a small price to pay to be rid of the reflux that was making my lungs dangerously sick.
As far as the weight goes...you can control that separately from exercise. There's a great program online (there's an app, too) called My Fitness Pal, which makes it extremely easy to journal what you're eating and keep track of what you're eating, as well as you exercise. There are others as well, but I settled on this one because it has a great app for my iPad. I lost nearly 10 pounds doing nothing but limit my eating and walking. Give it a try. It calculates calories, etc...once you get the hang of it I think you'll find it very easy. I'm still finding shortcuts and capabilities I didn't know it had. Just a thought.
You don't want to compromise the surgery that you've had. We all had some pretty big issues that led us to having a Nissen, and whatever inconvenience it causes is well, well, well worth it! People around here always remind each other that the surgery takes a good 6 months for most of the healing and a full year for the rest. I found improvements continuing into the second year!