Todd, practically ANY enamel-type paint, and all powder coatings I have used, benefit from baking the paint after application to cure it (outgassing of the propellant chemical, often Acetone unless it is a water-borne paint), to make it harder and make it adhere to the sub-surface better, whether the metal was primed or not.
Here's as good an article as any on it:
https://www.ehow.com/how_55340...ke-enamel-paint.html
It's a long-ish article and even gets into removing baked-on paint, so keep skipping over those pesky ads.
BTW, @edsnova: Using your covered grill as a paint bake booth was brilliant. I may keep the Weber I was going to sell and get rid of my counter-top toaster-oven instead.