Pics are a bit blurry, but I'm pretty sure that's the Carolina Sphinx moth, aka Manduca sexta, aka the moth whose caterpillars are tobacco hornworms. Hornworms grow quickly, eat lots, get really big, and can defoliate a solanaceous plant very quickly. Both tobacco hornworms and tomato hornworms (Manduca quinquemaculata) eat tomatoes, peppers, tobacco, etc.

Looks like it's laying eggs in that second pic. Check your plants for eggs. They're actually quite pretty--like little aquamarine globes. Squish them. Or I guess if you have a science-minded kid, you can keep them in a jar and feed them. They're pretty neat looking caterpillars. You'll have to check your plants carefully in future for signs of hornworm damage, which will look like normal caterpillar damage if they're still small and eventually lead to damage like this.

Thanks. I have had hornworms in the past. So I will be on the lookout for the eggs and hornworm damage.