Your character can carry up to 40 kgs.
The current inventory weight is calculated by item type and by slot, which means for example that a stack of 5 lumber will weights the same as a single lumber (as of patch #40).
When you try to carry something that is exceeding your weight limit, the game will display a warning in Area chat tab, just for you, and you won't be able to pick it up.
There's a known bug where you cannot move your stuff already in your backpack or equipped when you are close to this limit. It's probably because the game is taking it like you're trying to pick up the item you're moving.