If you NEED to change the route then you tell ATC what you need to do and they will facilitate it. If you merely WANT to change something for convenience then you request it and you may or may not get it.
Airways width is a funny one. The airway is allowed a certain width but the assumption is that the pilot will maintain as close to the centreline as possible. The pilot is to treat the airway as 0NM wide but it is designed with some tolerances applied. These tolerances are to account for navigation errors, they are not to allow you to deviate around weather, apply lateral offsets, or anything else unless specified in the applicable country's rule set.