Nestors posts are always 100% spot on and he covers most of what you need to know based on your question. One thing I'd clarify:

When he mentions level scaling, the world changed with One Tamriel. In the old days the game would keep you in zone one by giving you weapons that had 150 weapon damage and making monsters in higher zones too hard to kill. When they opened the world to you, they solved this by giving you damage and armor handicaps based on your level, so you can go anywhere and be able to survive/play. Now the game plays so that as you go up in level, your damage and armor goes up...but handicaps come off.

This answers you query -it's why your weapon's damage is weird. But it also introduces a very important concept: if you out-level your gear, you are going to SUCK. Lol. If you were a level 40 character wearing level 20 armor in olden days, you'd be weaker simply because you weren't enjoying the benefits of higher level gear. In the game today, you miss those benefits plus that gear gets weaker from having handicaps yanked. It's a double way that can DESTROY you. Try to keep gear within about five levels of your player level, and if you hit a wall look at your gear and see if it needs updating.

And be advised, no matter what, player levels 45-49 are now the hardest, in my opinion. It's a trade off with One Tam...there's a sort of dip in power at these levels that causes challenges for a lot of newbies. If you get to your 40s and start to struggle, don't freak out. Back off to some easier content and keep leveling. You'll hit vet and quickly get twice as powerful.

Based on your level, some add'l tips:

- Around level 30 you might move to green gear, minimum. Blue is ok if you have the skills/money. At level 40 I like to upgrade to blue. I'd recommend saving purple for vet, then probably running all purple from CP1-160. Four purple mats cost like $2000 in guild stores...you don't need to waste the gold by running purple all the time, but if you want purple gear it isn't that expensive to get mats.

- invest in hirelings when you can, and consider doing crafting writs when you can. Hirelings will deliver a lot of mats...they're good for purple down, and very occasionally bring a gold. Writs are the best/cheapest source of gold mats for gear. If you do writs, be aware that what you're being asked to make and where you drop it is entirely a function of how many skill points you've spent in the first passive. Read up on how writs work, then learn how to level things together so you can make what is needed without it being a massive pain in the butt. Why start writs now? A gold armor set requires 56 gold mats, which can be bought at guild traders for the oh-so-reasonable price of $450,000 gold. Or get them for free doing writs for a couple of months. Writs are faster.

- very important for you right now is learning how gear sets work. You have 7 armor slots, 3 jewelry and 1-2 weapon (depending on what type weapon you run). That's 11 or 12 slots. Success in ESO, especially as a vet, is about configuring these. Sets add powerful buffs and come in 5, 3 and 2 piece sets. Most add buffs for the 2nd, 3rd, 4th and 5th piece worn...but some also add a buff for one piece. I won't spoil anything or force you into a meta build, but my stamblade wears two 5-piece sets and a 2-piece set. This gives him what we might call seven "moderate buffs" (i.e., increase max stamina by 933) and three "major buffs". These buffs combined are far, far, far, FAR more powerful than what he gets from armor quality or most anything else.

- the damage you do upon hitting an enemy follows a formula with factors something like this: (weapon damage of equipped weapon) + (character total weapon or spell damage, depending on resource used for hit) + (max character capacity of resource used, i.e. Character has 34,000 max stamina for a stamina hit) + (if hit crits or not) + (any permanent passive that might affect that particular hit) + (any gear buffs) + (any temporary buffs from abilities or potions)

Yes, that's confusing. The point is that your weapon's damage value is just a piece of the dps calculation. Learning how to hit harder means learning the various systems at play and employing them strategically. For example, you're almost at a level where you can employ temporary buffs that increase your power by 20% (major brutality for stam, major sorcery for magic). Playing well above, say, level 40 means keeping your damage buffs up - "buy five get one free" is very powerful in hard fights.

Start reading tool tips and learning what your different abilities do. Turn on combat text and watch how different combos affect your hits. Look at your weapon or spell damage on your character sheet. Cast major brutality or sorcery and look again (quickly, before it wears off, lol). If you switch out a gear set, what is the difference in damage for your favorite ability? If you switch jewelry from items that add max health to items that add max stam/magic, how much harder do you hit? You don't need to cram all this in at once, lol, but start experimenting and learning how changes affect you, especially if you don't want to copy builds from online. (And your way is going to make you three times as good a player, guaranteed)

- you're good to start pvp-ing. You'll die a lot. I die a lot as a CP600 wearing like $2 million in gold gear, lol. Run with a group...a text chat saying LFG will almost always get an invite. Groups with mics are good for learning...you'll learn a lot from their blabber, ha. You might play a non-Champion Point campaign...this will reeeeeally help reduce your handicap. Go to keeps under attack and jump into the crazy. Turn combat text on and watch your incoming/outgoing damage - you'll perform way differently against humans, who are geared for it. Or stay away from busy areas and wander Cyrodiil...I love it, it's massive, there's great pve scattered in there and they did a great job designing it.

As with Nestor, those tips are catered to what I had to learn around your level. Hope they help.