This page of The Witcher 3 Wild Hunt has information on how to increase Geralt's load capacity. You will be able to carry more items without losing mobility.
Inventory in Witcher 3 has unlimited amount of slots in which you can place items. Sadly, it doesn't mean that you can collect new items with no limits. Geralt has capacity limit and if you cross it, he won't be able to run.
The default capacity limit is only 60 units and, since some armor parts or swords can weight few units, it's very easy to surpass the limit. Because of that, it is very important to increase the limit as you advance in the game. Interestingly, it isn't done by buying new skills. The only way to increase the limit is by buying new saddlebags for Roach, your horse.
Saddlebags can be obtained similarly to other items - by finding them in the game world, by buying them from selected merchants and by receiving them as a reward for completing some quests.
In the initial phase of the game, the best way to receive the basic version of the saddlebags is by completing the quest concerning horse races near the Crow's Perch. We have described them on the side quests in White Orchard page. By completing the race, you will obtain basic saddlebags that will increase your capacity limit to 90 units. Later in the game it won't be enough and at that point you should look for Zerrikanian saddlebags which are the best saddlebags in the game. They increase your capacity limit by 100 units, thus making it reach the point of 160 units. This will allow you to play comfortably without the need to get rid of all unneeded items after each journey.
In case of Zerrikanian saddlebags it is best to simply buy them. It can be done in Free City of Novigrad. You must complete the main quest Pyres of Novigrad to obtain access to the quarter of King of Beggars in southwestern part of the map. Go there, knock to the gate and enter the normally inaccessible part of Novigrad. You must find the merchant shown on the pictures above. He will offer you the saddlebags for around one thousand crowns. If you don't want to pay that much, you can wait until you reach Skellige islands. There you can win Zerrikaniam saddlebags in horse races.