So, each time I level up, It seems the damage displayed in my weapons' details gets lower. Ive only noticed this since approximately level 20. My Skyforge Steel Sword and Elven Sword (both Exquisite), each did 60 damage. Now, at level 24, with level 4/5 Armsman, they have decreased to 39. Is there some mechanic of the leveling system that I do not understand, or is this a bug?

Sounds like a bug.

I read that the sharpenings you do to your weapons will degrade. Then I read on the forums that they have taken out "buff" degradation.

Try saving the game, then crafting a new sword and sharpen it.

Last night before sleeping I gave a look around the interface and notice I have an active effect Rockjoint written in red that gives me -25% on melee. Are you sure isn't something like that?
I'm not sure if when you have it you can see the actual stats of the weapon damage.

Tried crafting a new sword + improving, same values. Don't have any negative effects at the moment either.

I should note, I had taken off my amulet of minor wielding, which when re-equipped brings me back up to 45 damage, but there still seems to be a major discrepancy.

Tried editing my level with the console, no effect on damage...

Maybe your weapon was enchanted but has now run out of charge?
Just a guess.

You did not mention whether you have any diseases. Check your active effects. Do you have anything that could lower your damage with 1H weapons?

For comparison, my epic glass sword does about 30 damage with only 1 point in armsman perk (+20%) damage. My 1H skill is not even 40, just almost.

Did mention that I have no negative effects above, but I could have worded it more clearly, sorry about that. Anyways, i've found the source; this is definitely the Armsman perk. I removed all but the first rank via the console and now im at 86 damage. Strange...

I noticed this seeing my ebony mace go from 105-78 damage. I realized I was wearing guantlets that increased 1 handed attack by 35%. Maybe you had a buffer item on.

I think this must have something to do with the percentage exceeding 100%, but that seems so simple...

Sounds like you had "Rock Joint" disease, which causes 25% less weapon damage. 75% of 105 = 78

It seems likely that the OP might have the same problem, but the numbers aren't quite right.

Dont have Rockjoint; no negative 'Active Effects' at all. Plus my character is a Werewolf Argonian, so to hell with diseases =D