Weight

Items that can be carried have a weight value which determines how many of them can be carried at the same time, and can affect movement speed. Weight also equals how many backpack slots it takes up.

This weight value is indicated by the icon in item tooltips. If no weight value is displayed, that usually means the item either has a weight of 1 or can't be carried.

The formula for how many can be carried is (capacity / weight) rounded down (to a minimum of 1).

Player
For the player, carrying objects will increase movement delay per tile according to the following table:

Bots
Bots incur a 1 second base movement delay (before modifiers) when carrying an object with a weight greater than their hand capacity, but are not otherwise affected by heavy objects.

Handheld Vehicles
For basic vehicles, carrying objects will increase movement delay per tile according to the following table:

Railway Vehicles
For railway vehicles, carrying objects will increase movement delay per tile according to the following table:

Animate Objects
Animate object such as colonists and animals can only ever be carried 1 at a time, and vehicles can only hold 1 as well.

They cannot be stored in a backpack. Colonist Seed is the exception, it is weight 1 and can go in a backpack, but cannot be put into the Mystical Stone Head.

Colonists technically have a weight of 1/2/8/16/32/48/64/80 depending on their tier, but they are always reduced back to tier 1 when removed from their shelter.