It's probably not going to be so cut and dry.
From the sounds of it "swapping weapons" will allow you to change roles.
The problem will 'probably' be obtaining whatever weapon grants you whatever abilities you desire.
Furthermore, I'm sure if a weapon determines so much, 'gear' in general will play a determining role in what you are 'capable' of ability wise. It's the only way I can see classes really being 'limited' while still giving you something to toy with and strive for (outside of a level based system).
Think FFVII's materia based system, just as an example. You needed two things to succeed (outside of levels). You needed gear with materia, and materia for that gear. You would build gear up with slots so you had more room for abilities, but the abilities were limited and controlled by the gear that allowed you to equip said abilities. This made it so you couldn't (for the most part) have control over everything in the game at once - you had to pick what a characters role would be, and equip gear and materia to make that role happen.
And to add complexity still, even though you can't 'level' in XIV, you can still 'learn' and 'grow' in certain abilities / skills. I'd imagine this would parallel the 'materia growth', where spells of a particular materia used over and over would get stronger.
This is all just hypothetical, and I'm in no way saying 'materia' or anything like it will be in the game, but 'idea wise' it sounds like what has been described to us.
Much the same way you can't become this or that in FFVII right off the bat, you will likely only get a 'sliver' of something to start off with in FFXIV - IE, if you choose the healer path, a starter healing spell that can grow (again, think of it as the game giving you a cure materia to start off with) - where you can branch out in other ways, but it will take time and effort to get there (think sphere grid of FFX).
Posting from just above the generator.