I bring a box, packing material, and a pre-paid UPS label with me to St. Louis every year and ship the big stuff back. I just take a guess at the weight and make sure I’m on the high side when I create my label. You could also weigh your box in the gym and print a label in the business center at the hotel. I’m always paranoid that I’ll lose track of time and miss the business center hours so I just do everything at home beforehand.
I drop my box off at the front desk before I leave and then request a pickup via my UPS account. They used to have a daily pickup but the past 2-3 years I’ve had to call it in.
I also take several empty plastic MTM cartridge boxes with me so I can take the smaller stuff (below .50 BMG) back in my checked luggage. I tape the boxes shut, and if I happen to have smaller rounds in the box that might rattle around I wrap them in toilet paper so that they are snug in the box.
I fly Southwest and I’ve never had a problem doing it this way. I think my bag has only been opened by TSA once in the past 10 years and even then there were no issues. I do send tracers/api/etc. back in the UPS box since those are not allowed in checked luggage as far as I know.