As others have suggested, this might not be really a problem. Others have mentioned the extra time and the spotlight that this player is flying. My initial concerns were about 1) if this PC does these actions in combat then it does not pull its weight helping in combat and 2) the realism of carrying 10 tons of material.
For 1Some people consider weight restrictions as a minor problem that they might be willing to give up. I've seen games where they do not care, they're looting everything, and computers currently carry 15 swords, 10 daggers, 20 javelins and 5 bows. When they return to town, they can say, "I will keep 3 swords and a bow in my personal chest, I will keep 2 swords, 3 daggers, all the bleachers and a bow, and I will sell the rest." And it's ok for some games.
If the problem of weight is not to be neglected in this game, then instead of saying "If you continue like this, I will apply weight restrictions," say "I understand that we all want to keep everything, but I do not do not really do it. feel like you are applying weight restrictions and keeping track of all weights, so be sure to at least stay reasonable. "And if that player pushes too far after that, you can just say arbitrarily at some point (without really keeping track of weight, but just because it's outdated)" When you pick up that sword, you realize the weight of all yours is a bit too much. All this weight unbalances you. If you do not do something, you will move at a reduced speed and you may notice dexterity problems. "
For 2: Why is it acceptable that this player does not help the fight, especially as a melee combat class? Are battles too easy for this to be of no importance? If this is the case, change the balance of the battles. Is help needed, they barely survive, but does this PC continue to do these things anyway? Then the other PCs (the characters first, not the players) should shout at him. If that does not work, you could have a conversation outside the character between the players under the pretext that this player does not help them in their role.
Player 1: Orcsmash's eyes illuminate at the sight of the bandit leader
bulky wallet, and he tries to tear it off.
other players sigh and make comments
DM: To roll.
DM: (whatever the result)
Player2: Magicdude is about to burst a vein and he's screaming at Orcsmash,
"Guy! What are you … doing!?! Put your head in this bloody fight!
If I lose a hand because of you, I swear that you will be the next target of
my biggest curse, and that's if I do not eclipse your —
And be sure to let the other player say what is needed, even if it sounds too much to say in a round, as long as the speech is not long, of course. At this point, you can insist, outside of the character, so that the other player plays at least his character in order to help the group at best, and insist that combat flights be avoided when it might put the party in danger. .
If that does not help, they may have to follow through on their threats. And / or, maybe the characters decide to no longer want this barbarian and prefer to replace it with someone who pulls all its weight. If that goes so far, the same player could even play the new PC that replaces the old one, and maybe even be essentially the same character, with just a different name and with the insistence that this "new" "character does not neglect his fighting duties.