You're still dealing with very different games. Demon's Souls is mostly linear with a level select. Dark Souls is a comparatively nonlinear game which is specifically built to make you want to run around and explore. It really would be like adding item burden to a game like Metroid Prime. I don't see how making "Should I backtrack to the bonfire to dump the stuff I've found" an omnipresent burden on players is going to enhance the most important aspect of Dark Souls aside from combat.
Did you like item burden in Demon's Souls? If you didn't, then yeah, it makes sense that you wouldn't want it here either. However, I don't Demon's Souls and Dark Souls are different enough to warrant the removal of item burden, if you enjoyed it.
I don't think Dark Souls' non-linearity is that different in relation to Demon's Souls. Sure, there is the occasional shortcut exception, but for the most part, if you head in one direction, you're basically going to be "doing that level". It's not fundamentally different from the level select in Demon's Souls; they've just made more subtle.
Also, you can think of backtracking as the price you pay for picking up something heavy (which is usually something good). You can choose to continue onward, and hope you don't come across more heavy equipment, or you can play it safe. It makes finding items a harrowing decision-making event, not just strictly rewarding. Additionally, there were a few moments I recall off the top of my head when I could just bumrush past a monster, grab the item, and die. With item burden, if you're holding too many things, you wouldn't be able to pick up the new item, it would be automatically dropped, and so when you die, it would disappear forever. This eliminates that whole cheesing factor.
Besides that, I will say that even the equip burden is screwed in Dark Souls. You should never be able to ninja flip with heavy sets like Giant/Havel.
In Demon Souls ninja flip didn't exist but even the normal flip was impossible with Brushwood set.
I hope From will bring back item burden in the next game and think more deeply how to balance the game.
Yeah, I always thought the ninja flip ring should have been restricted to 25% or less burden. Basically, it should be a buff to people who already have the best roll. The way it's currently implemented, it will definitely stay the most-used ring, bordering on necessary for PvP. Unfortunately, I don't see Namco ever forking over the money to make another patch. For the most part, the current Dark Souls build is pretty well-balanced, and I think I can be content with its current state.