Inventory is managed using item slots, not item weight. These abstract slots represent the combined storage capacity of your bags/belts/weapon sheaths/etc—the more item slots you have, the more items you can carry.
To calculate your character's inventory capacity, first check your character size—the bigger you are, the more space you have about your person to carry items.
Next, check your character's strength — the stronger you are, the more items you can carry. You gain (or lose) a number of item slots equal to your STR modifier.
Armour is big and bulky - the bigger the armour, the less inventory space you have for other gear.
Wearing armour means that you can't carry as much, but there is a trade-off—you become more resistant to harm. If you are wearing medium or heavy armour—and you are appropriately proficient—you gain the following perk:
Medium Armour: Reduce any bludgeoning, piercing, and slashing damage that you take from non-magical weapons by half your proficiency bonus (rounded down), to a minimum of 1.
Heavy Armour: Reduce any bludgeoning, piercing, and slashing damage that you take from non-magical weapons by your proficiency bonus, to a minimum of 1.
This perk doesn't stack with any additional armour feats or bonuses you might gain — use the highest value.
You must draw an item from your inventory before you can use it. During your turn, you may use your one free object interaction (PHB p190) with your inventory to:
Add/sheathe one item (or collection of tiny items).
Remove/draw one item (or collection of tiny items).
If you find yourself carrying more than your inventory capacity allows, you are encumbered. While you are encumbered:
You have disadvantage on all rolls.
Your speed is halved
You gain hunger, thirst, and fatigue at twice the rate.
In addition to item slots, your character can freely carry one ration box, one waterskin, and one purse. These don't occupy any slots and can store a small amount of basic supplies — food, water, and money.
Ration box: Stores up to five basic food rations.
Waterskin: Holds enough liquid for five drink rations.
Purse: Holds up to 100 assorted coins.
While these extra containers don't occupy any item slots, they can still be affected by NPCs and monsters — stolen, damaged, destroyed, etc — so beware.
Worn items, such as gloves, boots, hats, bracers, etc — with the exception of armor — don't occupy any inventory space until you unequip them and put them back into storage.
Item size is measured in slots, telling you just how much space an item requires in your inventory. Items generally fall into one of four sizes: tiny, small, medium, and large.
You can store up to 5 tiny items, 5 gemstones, or 100 assorted coins in a single item slot.