There are no zero weight containers, but if you join the thieves' guild in Verdistis you can find one there which only weighs 5 units. Until then, there are sacks of grain you can use as containers, which weigh 100 and are also small graphically.
There is a potential problem dropping things directly into a container in your inventory (particularly if you are doing a lot of looting that way);
weight bug and disappearing chests
