Geordie Ross said:
Does the energy from the sun get converted into biomass? If so, how much extra weight is added to the Earth every year?
Well... Kind of.
Biomass refers to the mass of biological organisms in a particular area. The area does not have to be geographical. It can be, for example, the plants in a forest as compared to the animals in the same forest. Or the pine trees as compared to the maple trees in a forest. Or the termites in a termite nest as opposed to the other organisms.
Total biomass on Earth is many billions of tons.
As others have pointed out, the sun's energy, even when captured, will produce a tiny effect. Recall the equation e=mc^2. So to get 1 kg of mass you need 9E16 Joules of energy. Plants are about 1% efficient fixing solar energy. The Earth presents a disk to the sun of about 6000 km in radius and the solar constant is about 1 kW/m^2. And quite a bit of the planet isn't green plants. So the mass gained is something less than 0.1 kg/s. This is to be compared to the mass of all living things on Earth, which is extremely large in comparison.
Also, as others have pointed out, this is (very nearly) equal to the heat losses from the Earth. If it wasn't, the Earth would be heating or cooling to match. (The differences is primarily down to energy stored as biological material like coal, peat moss, limestone, etc., plus some changes in temperature.) So the net is very nearly zero.