Level up your protectors reputation and buy backpacks, later on you can also buy some backpacks for your mount that also increase your weight. In winery crossroads you can rent/buyout a tavern room where you can store some of your items.

I once gave a little more detailed response here:
dragoneternity.com/forum/drako/8290.html#cP=1

i have never played any game with such low inventory* <---makes more sence

Bones420i have never played any game with such low inventory*
It gets better in the long run - the very long run.

get a mount, put bags and saddles on it, the best it will accept. When you upgrade to a newer mount usually the very next level, leave your existing mount equipped. Buy new gear for your new mount. Continue this as you keep getting newer mounts. This will increase your backpack substantially. All the bags and saddle space stack so you keep adding new capacity with each set of new gear for the new mounts you purchase.

(this is something you tend to learn as you play) you can always go back and use that lower level mount when you want to be mounted on a cheaper beast for different things such as heroic or fort runs etc...