While under the effect of blessings, I equipped a few weapons that I can't equip otherwise. Is there any penalty if I continue using them after the blessings wear off?

They should de-equip after that (though I didn't try that, you are free to).

Keep in mind, later in the game those blessings will become permanent (if you won't sell items which have huge price tag on them, but sacrifice them in places like that one statue of Febret in the woods).

Actually, they didn't de-equip for me.

That's great. But as I said, eventually those blessings will become permanent, so it isn't that big of an exploit (but still it is exploit).

If you don't meet weapon requirements and raise your stats with equipment that gives +Strength/Agility, if you remove the equipment (rings, whatever) your weapon gets unequipped automatically. If that doesn't happen when the blessing wears off then it may be a bug.

The game did eventually unequip the weapon, but it took a while. Incidentally, my Gaulen is only one point of Strength short to equip the weapon and has enough experience to gain a level, so guess which stat of his I am going to raise (other than Speed).