Thank you all for all of your tips. I decided to try using twine and soak it in watered down glue before applying it to the balloon. It turned out much more sturdy than the first time and it looks a lot better. The film was still there but not nearly as much as it was the first time, so removing it really wasn't that big of a pain.
I also found a shorter string of lights at a yard sale and decided to try them instead of the regular length string lights I used on the previous one. Those ended up being MUCH better because they didn't weigh the twine down at all. I would like to use the LED string lights but I am still not sure where to find them in the shorter lengths and also at a reasonable price.
Here's the image of the newer one::
I think it looks a lot more clean than the other one, but I'm sure it could be better, so if anyone has some tips on how to improve it, please feel free to comment!! I can use all the help I can get!