This page of the Mr. Prepper guide contains information about carrying capacity, that is, how much your character is able to lift.
There are two ways of increasing carrying capacity in Mr. Prepper. The first is to increase the trust level with Bob, the mine trader. At the first trust level already, you will be able to buy Atlas Jacked for $100. This will increase your carrying capacity by 20 from the default 100. At the third trust level, there'll be another book to buy: Atlas More Jacked ($180), which will increase carrying capacity by another 20 units.
The second option to increase the carrying capacity is to craft a backpack. It is available on Level 2 of the Workbench and costs 5 Fabric. In the beginning, you can get fabric by buying a carpet at the Jetsons' house or a carpet from Jenny, which you will lay in the house, thus destroying the one you already own. The backpack provides an increased capacity of 40 units.