Today I decided to cure my vampirism, which was given by Lord Harkon during the vampire quest line in Dawnguard. I noticed that there was no "weakness to sunlight", which was amazing. I thought it was a Vampire Lord trait.

After finishing the quest line, I decided to cure vampirism. Fine.
After a while, I decided to get vampirism back because my illusion spells were not as strong while using it on my undead minions. So I got Serana to give it back to me.

After that I noticed that my magicka was not regenerating during the day, after looking at the active effects... "WEAKNESS TO SUNLIGHT".
I reloaded a previous save when I was about to decide between dawnguard and vampires, and the same happened after Harkon bitten me: No weakness to sunlight.

Is it normal or a bug?

prob a bug

As a vampire, no matter what the source, you are supposed to get a -100% regen on health, magicka, and stamina while in the sun.
The weakness to sun not showing up is most definitely a bug.

It's a bug probably. I still have a weakness to sunlight when turned by Harkon.

That's weird. My savegame has nearly 300h of gameplay, so it was probably triggered by an old bug, like many other bugs I got after all these updates.
Plus it's been 4 months to get there, no way I'll lose another 4 months on a new save. lol