The base rules don't define a mechanism for how this would happen. An optional rule does, but the cow's weight is not a factor
The basic issue in the base rules is this: Conjure Animals describes how the caster summons animals at a given point in space. You can pick a point in the air, sure, so so far, so good. But the spell does not say anything about making an attack, which is where we run into a problem.
Attacks generally have details which simulate the attacking character trying to hit their target in a meaningful way and with a chance of failure, such as rolling a d20 and adding the appropriate attack modifiers to try to beat the target's AC. Some attacks are presumed to hit, but give the target an opportunity to avoid damage, such as making a saving throw. Some attacks always hit their targets, like Magic Missile.
The problem with the meat-eor plan is that the spell doesn't involve any of those things. There is no method for how you would determine if the cow is appropriately placed when summoned-- there is no attack roll, and so there is nothing to compare to the target's AC. There is no presumption of automatically hitting with a chance for the target to make a saving throw.
So the weight of the cow is a non-issue. Even though the plan would have some chance of working in real life (with a few modifications to what constitutes "real"), the game rules don't provide any way to figure out if this would hit a target. And this is before trying to figure out how much damage should be dealt by having a large object fall on a target without having any damage dice assigned to it.
So, the base rules as written do not permit this. The spell doesn't work that way, and none of the elements of the plan are defined in game-mechanical ways that allow us to reliably determine any of the plan's outcomes. That said, if you work with your DM to figure out mechanics for it, then you can do it. There is guidance in a supplement, detailed below, if your DM is inclined to allow it.
Optional Rules: Tasha's Cauldron of Everything
Tasha's Cauldron of Everything does, in fact, offer a way to determine if a target is hit and damaged by another creature falling onto it from above. It's up to your DM if this optional rule is used, but it does offer a way to adjudicate this in the way you're hoping. The optional rule for falling onto a creature states (TCoE, p. 170; "Chapter 4: Dungeon Master's Tools"):
If a creature falls into the space of a second creature and neither of them is Tiny, the second creature must succeed on a DC 15 Dexterity saving throw or be impacted by the falling creature, and any damage resulting from the fall is divided evenly between them. The impacted creature is also knocked prone, unless it is two or more sizes larger than the falling creature.
The maximum damage you can expect is unrelated to the conjured animal's weight. The conjured animal suffers 1d6 damage per 10 feet it falls, so if the caster conjures the cow directly above itself at the spell's maximum range (60 feet) the cow can accrue 6d6 damage dice. This translates to a potential maximum of 3d6 damage dice for the creature struck by the cow.
3d6 damage is relatively underpowered for a 3rd-level spell slot, so there shouldn't be any concerns about balance.