Calorie advice.

What is your re-supply frequency?
What flexibility will you have on what is in the next drop?

Predicting, especially over only a three week period, is pretty tough.

Chances are you will do fine on 2500 – 3000 calories for the first week or 10 days, then ramp up your mid-day snacks as needed.

The trade-off is carrying unneeded food weight versus loosing some weight until you get it dialed.

It's your call.

You list your pack weight with food at 40 pounds. What's your base weight? Do you plan on resupply or do it all in 25 days? (the CT is 500 miles divided by your anticipated 20 miles a day)

Maybe we should visit your gear list first. Then look at your itinerary for the hike. THEN worry about calories. But a short answer on calories–1.2-1.6 pounds of food per day is what I understand to be a good goal. Don't know calorie numbers….

My experience of long distance hikes is limited to one. But on that journey of 1000miles I carried 2.5lbs/day. In the beginning I was stuffing myself and burying extra; at the end, I was still hungry. We all have our own personal relationship to hunger, but for me, I would hate to jeopardize my hiking enjoyment by being hungry or listless, or whatever it is you become when your body is anxious for food. Whatever you start with, plan on increasing your rations gradually after about a week, or ten days.

If you're quite extreme (as some contributors, or even founders, of this website), you could try to put on 10-15 lbs beforehand, planning to burn it off. Probably against doctor's orders, but its also surely what our species did as a matter of course before agriculture; why not put those vestigial storage genes to good use!

Assuming you're male, you may need upwards of 3000 cals per day just to maintain weight, maybe more if you have a particularly fast metabolism. Since you are already borderline underweight to begin with, you might want to err on the side of caution and plan on 3500 cals per day. Either that, or pile on some extra weight now so you can carry less food weight, though this risks spending some time hungry which is not always fun or productive if you're doing big miles.

"Any advice on nutrition for a new lightweight backpacker and a new thru-hiker would be much appreciated! Please throw every resource you have at me!"

I would recommend that you visit the Arctic1000 website and read through the information on food there. What they chose to carry, how much they chose to carry, and how it was distributed over time, along with the rationale behind their choices, makes for very informative reading for someone planning a trip such as yours. And yes, they did bulk up ~15# before their departure. I, personally, don't consider it extreme at all but, rather, a very intelligent approach to minimizing the amount of food carried in their packs and, therefore, the pack size required for a 600+ mile unresupplied trip.