Henry Dobbins carries his girlfriend's pantyhose. He keeps them tied around his neck, supposedly for good luck. Ironically, he continues wearing the pantyhose even after she dumps him, saying that they're still lucky. Maybe he likes the way they feel around his neck. Or maybe he the pantyhose are simply his strongest connection to home, and he is unwilling to let go of how they have made him feel.
This goes back to the "things" these men carrying having more than just concrete weight associated with something. For these men, everything they carry has a certain "weight" attributed to it. For example Dobbins panty hose weigh more than the 1 lb concrete weight. They weigh more because they symbolize home or love; even if that was in the past, there may have still been love there. They are also a shield or a symbol for a more literal meaning that just panty hose. If you begin a journey or an experience with something, you don't feel right when you don't have that "thing" with you. This could be transcribed in all areas and aspects of life.