Good question. I never really "got" the skills / level thing in Skyrim and other TES games. As I recall, there, you could raise your blacksmithing skill by crafting iron daggers over and over and over and over and you'd have like 100 blacksmithing skill, which is all well and good... but your COMBAT skills would be level 1 - 3 or whatever they were just from the few fights you'd have to do in the opening parts of the game. Your LEVEL would also be increased because your SKILL increased. So you --- and more importantly, your foes! ---- would be higher level but your combat skills would still be very very very low. So you'd have a very hard time of it.
I'm reasonably sure that leveling-xp is tracked separately from skill-advancement-ranks so that you could have a high rank in a given skill and yet not have a high LEVEL, although there may be some kind of cap, like you can't have a skill greater than, say, 2x your level or something. I Dunno (obviously).
Main reason I'd like some clarification on leveling xp / skill "xp".... is that I wonder if it would be advantageous to level up multiple skills at the same time, or if that would somehow increase your raw level, and yet your skill in any one weapon would be LESS than if you had focused on one weapon exclusively. And if you DID focus on one weapon exclusively, and then wanted to change to a different weapon, your skill with that weapon would be WAY lower than your "main" weapon.
Not really sure having a low / high weapon skill factors in, anyway. I mean, obviously you have to have a given skill rank in order to unlock a particular skill "power" / ability that you put on your hotkey bar. But if you have only class/race skills slotted on your hotkey bar, and don't use any weapon skills in the hotkey bar... then what does your skill rank in that weapon DO, really? Does it increase your damage? Your chance to hit (behind the scenes, since we know you have to 'aim' to some extent to hit).