The app is only downloaded once every month or two for the usual updates. It happens in the background when you aren't using your phone anyway, and by default both OSes will wait until you're on wifi too.
App size doesn't matter much in the actual use of the app, especially if you're using it often.
I don't expect it to fetch everything from a server every time, not every app needs to be only a browser serving remote content. I just expect a simple app to be simple in size, there just isn't much going on in this app.
... except that the complete collection of everything the UPS app needs to execute or display, in order to actually fulfill its function, summed up throughout all of its operation in every possible mode, probably fits in 1MB. If there's 100MB of stuff you store or potentially download for a shipping app, then you're including something that doesn't add value for the user.
Start by removing all the pictures, videos, and similar. Then take out the analytics crap. Then, if your app is still big, figure out what's wrong with your code.
There are two conflicting problems here that are the two heads of the same coin:
>"Why is this app so big, don't the devs respect my storage?"
vs:
>"Why is this app so slow, don't the devs respect people with poor connections?"