Calculate carry capacity, encumbrance thresholds, and push/lift limits for any character or creature
Carrying weight in DD 5e is quite easy when you understand the basic rule. Carrying capacity of player is its Strength score multiplied by 15. That is the weight in pounds that the player can carry, and it is quite high so most players usually must not care about that.
So if the Strength is 12 that player can carry until 180 pounds. If player has 17 Strength, it carries 17×15, which matches 255 pounds. Everything you carry counts in that amount; every object adds its weight to the total.
Players also can push, drag or lift weight in pounds until double of his carrying capacity, that is 30 times of his Strength score. If the weight surpasses that limit, you simply can not move it. Some races, as firbolgs and goliaths, can handle double normal weight: they can carry until 600 pounds and push, drag or lift until 1,200 pounds without requiring an abiltiy check.
There is also a variant rule about encumbrance. Objects that you must carry with two hands have weight of 2 or more. Until the Strength score of the player it is unencumbered, until double of the Strength it is encumbered, and until triple of the Strength it is heavily encumbered.
While you use this variant, you can ignore the Strength column in the armor table. Each can wear any armor regardless of strength, on condition that they are proficient, but the weight however tends to brake them.
But here the cause about weight: it is only a bit important compared with the space in bags. Player with 20 Strength can carry 300 pounds, so technically it is possible to carry 7 half plate armors. But where exactly do you keep them?
Even if carrying 14 halberds stay inside the carrying capacity, where do they actualy go? Hence spells as the floating disk of Tenser exist, and hence buying a wagon and mule for hauling loot are wise early purchases.
Rucksack is leather bag worn on the back, usually with belts to set it. One bag can carry 30 pounds of gear. To count how much fits, subtract the weight of the rucksack and its content from the total carrying capacity, and later count the remaining space.
Trace precise weights of enormous bags of coins and gear genuinely can slow the game, if you too focus on it. If the DM wants that carry weight and encumbrance genuinely matter, it requires better system for tracking that and better character sheets for managing it. Some groups use spreadsheets that automatically update the weights of objects, weapons and armours.
Carry weight most commonly matters when players try to use Strength as dump stats or try to carry silly amounts of treasure. In many campaigns, players get access to bags of holding quite early in their careers, which mostly settles the problem.