You most likely won't have any trouble. The big thing is food management in camp. Never ever put food or eat in in your tent. Rodents to racoons to bears may try to get into the tent. If bear lockers are available, use them otherwise you will probably not see a bear. Chipmonks and racoons can chew through anything panniers, tents, etc.
I carry a "opportunity" lock to prevent thefts when in larger towns or cities. The lightweight lock is a 1/8" vinyl coated wire with loops on the end. I use a very small lock. It is about 12 feet long so I can wrap around anything and include the pannier handle loops too. Again, it is to prevent a theft where someone walks by and sees and opportunity. A pro (which we luckily do not have much of in America, especially on the TA) can get any bike.
Note than on Sundays it is not uncommon that grocery stores, restaurants, etc. are closed in middle USA. Always carry an emergency supply of food. Doesn't have to be much, just a couple of granola bars or the ever present peanut butter and tortillas.
Weather should be fine. Just get a weather app that has a radar. I use WeatherBug. Do what the locals do, especially during a tornado watch. A watch can cover a very wide area and the nearest "possible" tornado can be 50+ miles away going away from you. However, if the sky gets greenish, look for cover as that means a lot of hail is nearby. If it is a hot day, the hail can be the size of a golf ball or more. Not fun at all.
Other than that, enjoy the trip. Tailwinds, John