Hi and welcome to the forum!
In general, I would ask about any mods you might be using and for a save (please attach both save files in an archive).
However, based on your description, I'd say everything works as intended.
The skill number provides a bonus in addition to the base damage of a weapon / skill /spell, which does not change - thus, the better the weapon, the higher the bonus will be.
For the game, it means you have to upgrade not only skills, but also weapons, armour, arrows, and spells.