As others have suggested, this might not be a big problem. Others have mentioned the extra time and the focus of attention that this player is stealing from the game. My initial concerns were about 1) if this PC performs these actions in combat, then they are not doing everything possible. in helping with combat and 2) the realism of carrying 10 tons of equipment.
For 1Some people consider that weight restrictions are a minor problem they may be willing to give up. I've seen some games where they do not care, they plunder everything, and PCs currently have 15 swords, 10 daggers, 20 javelins and 5 bows. When they return to the city, they can say "I will keep 3 swords and a bow in my personal chest, I will keep 2 swords, 3 daggers, all the javelins and one bow over me, and I will sell the rest". And that's fine for some games.
If the issue of weight is not something that should be overlooked 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 really do not" . I want to enforce weight restrictions and keep track of all the weights, so please, at least, keep it reasonable. "And if that player pushes you too far, you can say it arbitrarily at some point (without tracking of no weight, but because it is more than reasonable) "As you raise the sword, you realize the weight of all your is too much. All that weight makes you lose your balance. If you do not drop something, you will move at a reduced speed and you will notice problems with your dexterity. "
For 2: Why is it acceptable that this player is not helping in combat, especially being a close combat class? Are the battles too easy so it does not matter? If so, adjust the balance of the battles. Is the help needed, just survive, but this PC keeps doing these things anyway? Then the other PCs (the characters First, no playersI should shout at him. If that does not work, then you might have an unusual conversation among the players because they are not helping with their role.
Player 1: Orcsmash's eyes light up when he sees the bandit's leader
Bulky purse, and try to snatch it.
Other players sigh and make comments.
DM: (whatever the result)
Player2: Magicdude tries a burst in a vein and screams at Orcsmash,
"Dude, what are you doing? Put your head in the damn fight!
If I lose a hand because of you, I swear to you that you will be the next target of
my super strong curse, and that's if I do not make a ray of you —
And be sure to let the other player say what is necessary, even if it seems too much in a round, provided it is not a long speech, of course. At this point, I could insist, outside the character, that the other player, at least, interprets his character in a way that helps the party, and insist that he does not take out more pockets in combat at times when I could put the party in danger.
If this does not help, maybe they should go ahead with their threats. And / or, maybe the characters decide that they no longer want that barbarian and prefer to replace him with someone who takes charge of his weight completely. If it goes that far, the same player could even play the new PC that replaces the previous one, and maybe it could be essentially the same character, just with a different name and with the insistence that this "new" character does not neglect His duties of combat.