You can adjust your backpack space by adding to the "BlackMarketUpgrades" section in the "Raw" tab. Line 8 is backpack space and line 9 is bank space. You can no longer go above the maximum 27 since the latest update.
Hey there, new forum user, old forum lurker, big time Borderlands fan. =D
A shady way you can use to have lots of bank space using Gibbed is to copy paste a weapon several times in the editor. This way, it'll "bypass" the limit, and all you have to do is switch the weapon you want to safekeep with one of the copied ones.
If you want to expand your backpack, sadly, it's how blakwidowstang said, you won't have much luck there. =\