Wood fetchers, in my opinion, should be sturdy enough to carry a heavy load of wood and light enough to add almost no extra weight.
I made this wood fetcher/wood basket in five minutes using things that we already had at home: a left over piece of a wooden shelf, a piece of a broom stick, some stainless steel mounting band and screws.
The wood shelf is about 60 centimeters and the broom stick a little over 50 centimeters. They can be a bit shorter as it will get very heavy when it’s fully loaded. Each piece of mounting band is around 1 meter. Fold the band in the middle over the broom stick and attach it with screws. Then screw the ends to the sides of the shelf.