It depends on why you're playing AD&D and what kind of game you're running. Do you and your group enjoy the challenge of tackling mundane problems in-game, like how to best navigate the Swamps of Miredom, whether to risk the mountain pass before the spring thaw, or where to find a buyer for a two-tonne gorgon carcass?
If playing people trying to get by and turn a profit on their strength and wits is your group's thing, then by all means go full-on with the encumbrance rules and let them enjoy trying to figure out how to pack and transport that dragon hoard, how to guard and secure the remains between trips out of the dungeon against the scavengers and opportunists come to steal some of it away, and how to store, trade, sell, or otherwise make useful the treasure without getting scammed Gold Rush–style by people raising their prices to profit from the haul. If you know your players enjoy this kind of problem-solving they still might grumble if you enforce encumbrance scrupulously, but just remind them that there's no challenge to getting the treasure home if they can all just carry infinite gold on their backs.
If this is the way you go, you can make it easier on everyone by adopting a coarser-grained encumbrance system that still tracks every item but not by pounds. Some of the latest D&D retroclones have adopted a "stone weight" encumbrance system, where items are tracked by the stone (~10 or 20 lbs). I believe the original implementation was in Delta's D&D house rules, and a retroclone that implements a variant of stone weight is Adventurer Conqueror King. In these systems, stuff below 1 stone tend to be bundled (e.g., arrows) or you can carry X of them before you have to add 1 stone to your carried weight (scrolls, etc.).
Alternatively you can use a "slot" encumbrance system, to really emphasise the bulkiness of stuff and the importance of where and how you pack things. Untimately proposed such a system in blog post that you could use. Torchbearer and Lamentations of the Flame Princess implement such a slot-based encumbrance system as well.
If your group is more about the heroism and story, then probably playing encumbrance by ear or hand-waving it entirely would be better. They still might enjoy the occasional strict-encumbrance challenge, but when it's the exception rather than the rule it can be a nice, special challenge without becoming tedious. (This is where your skill and judgement as a DM will be put to the test—judge your players right and they'll love it even while complaining; wrong and they'll hate it.)
However, I've found that playing encumbrance by ear is a pretty solid strategy as a DM. If you get in the habit of asking the players where they're carrying all this stuff—have them describe how they're dressed and how they're carrying all that gear—you can make judgements as necessary when it matters to the game play / plot / task at hand, and levy a penalty (or bonus) that suits you. Then the benefits are several-fold:
- It increases the players' sense of immersion a bit to imagine what this ready-for-anything hero actually looks like with all that stuff.
- The players are subtly reminded that they can't just carry everything—the fact that you're asking implies that their answer might have consequences.
- The players will start to moderate what they carry to what is "reasonable", not wanting to get caught over-loaded when you ask at a critical moment.
- You can tweak how much encumbrance matters just by asking more or less frequently, at more or less important moments, and by handing out larger or smaller modifiers. (Don't forget to give characters a bonus if they make a point of unloading before trying to be stealthy!)
This "encumbrance system" worked for me in a game of AD&D where I wanted the game to move swiftly, but I also didn't want the players ignoring the downsides of having too much gear and trying to carry too much loot. When I wanted them to feel the strain of fleeing certain death while hauling around a magic stone head, I wove their struggles to hang on to the thing into the way I described the action, making it obvious that their choice to keep it might be their downfall at any moment if they made a misstep. If I'd been using strict encumbrance then they probably couldn't have carried that stone head with the rest of the things they carried without being a few pounds into the "overloaded" category, and it would have been obvious that they couldn't reasonably choose to take it, but it was far, far more interesting a game when they could choose to take it with them, but at the constant risk of it slowing them down at a critical moment.