In Kingdom Come Deliverance your inventory limit (weight limit) is determined by your strength statistic.

You get roughly +10 inventory size per strength level.

So how do you increase strength?
Through combat.
Every time you fight/defeat enemies in melee combat you get a little bit of XP towards this stat. You can check this in the pause menu > player > strength.

Bonus Limit increase from Skills
Unlocking the strength skill "Mule" gives another +15 pounds weight increase for your inventory! You can buy this in the strength skill tree after reaching 4 strength.
There's also a Mule II skill that gives +20 pounds (strength level 8) and Mule III that gives +24 pounds (strength level 12).

In the early game your best bet is to get to 4 strength quickly by fighting a lot with melee weapons. From strength 2 to 4 you get roughly +20 inventory limit increase just from the level-ups. And then buy the Mule I sub-skill for another +15. This way you can carry 97 pounds quite early in the game. A big step up from the 60-something you start with!

Saddlebags
You can also store your inventory items with your horse. You get your own horse automatically after main quest "The Prey". Only then you can transfer items from inventory to horse.

Your horse can carry 150+ pounds with a normal saddle. If you buy a better saddle with saddle bags (at horse vendors), you can increase this limit.

Simply press Square (PS4) / X (XB1) on the inventory item you want to send to your horse. You can then swap it back from the horse to your own inventory at any time. This is also great to reduce your inventory weight. If you want to bring a lot of arrows or different armor sets on a quest, simply store it with the horse and then swap it back to your inventory when needed!

You can also store loot (armor from dead bandits etc.) with your horse. This is great to bring back armor to town and sell it for quick profit.