If the Army Psychologist's office took one look at Hightower's footlocker he'd be given an immediate section 8. It goes beyond "perfectly spotless" into a kind of organizational Nirvana. Hightower must control his environment to the last detail, lest he go into fits.
As a long range sniper, he sees the battlefield as a teeming chaos that need order imposed upon it. The Barret light 50, with a one mile range and the ability to shoot through hard cover is a powerful tool for imposing order.
"Yes Black Flag, I will carry your extra ammo belt, but if you don't put your kit in order, I'll shoot you myself!"