There doesn't seems to be a limit in the weight of the items you have in your inventory, however there is a limit of 1984 items in total, not counting keys and scrolls. For stackable items, there is a limit of 99 copies of each stackable item.
There are however many different items, including many weapons and piece of armor. Keeping all of them in your inventory at all time can make switching of equipement difficult. The merchant Domhnall of Zena that is located in the Depth sell a item called Bottomless Box. It has the following in-game description:
A peculiar bottomless wooden box.
Its origins are unknown. Some deride
it as a symbol of unbridled avarice.
Any number of items can be deposited into
the box, and items can be managed while
resting at a bonfire.
It allow you to store item in the box at each bonfire instead of carrying them with you. So if there is any limit to your inventory, you can bypass it via this item. And if you want to keep all the stuff you find, but like to switch of gear depending on the situation, this may be the solution to your problems.