Do DLC weapons level with me?

I opened the Bonus Content chest at level 17, and they were all basic level 1 gear. I then tried playing with them on a different character until level 4 or so, and they stayed the same.

Gear you get from purchasing DLC is nothing but starting gear. It does NOT improve at any point.

Certain DLC level up along with the player, if left in non-accessed state at least - one time I did not touch DLC items until level 35ish, and at least with certain items, an indisputable leveling up had indeed occurred... "Special Delivery" items are case-by-case, and I believe, the amalur Wiki-fandom and many other websites, enumerate which specific ones are dynamically capable of being leveled, which specific ones will level up (if opened later), and which ones, not behaving so... I hypothesize tentatively the items the Amalur merchants are averse to paying one penny for, will be the items not scaling to one's level and lamely fixed...