The main type of carbon fiber used for the manufacture of bicycle parts are normal tow (under 12000 fibers) carbon fiber, like T700, or commonly known as 3k, 12k weave, and UD(uni-direction) carbon fiber.
carbon rim 3k 12k ud
carbon fiber weave 3k
carbon fiber weave 12k
carbon fiber weave UD
Bicycle components, specifically carbon frames & rims are made using various grades of carbon fiber characterized mainly by their tensile strength and tensile modulus. Tensile strength is the amount of force needed to cause the fibers to break, while the tensile modulus is a measure of the carbon fiber's stiffness.
The cost of carbon fiber goes up with the increase in tensile strength, or increase in tensile modulus. And for carbon fiber weave also determines the cost of material with larger weave prepreg (eg.12k) costing less, due to the lower cost of manufacturing.
Carbon fiber layer(prepreg) has maximum strength only along the lengths of the fibers. That is why almost all the inside prepreg are using uni-directional carbon fiber while making carbon rims & frames. But the inside layup charts are still not identical. For example, the orientation are different( some are placed at 0 degree, some are 45 degree, 90 degree). This is very important to make carbon rims & frames with good strength & performance. That is also why using uni-directional fiber instead of woven carbon fiber (eg. 3k, 12k) creates stronger frames & rims.
Thus, the main use of woven carbon fiber is for appearance. But there is one mechanical benefit for 3k woven carbon fiber. Putting the 3k woven carbon fiber around hole area, it can prevent carbon fiber from laminating while machining holes.
For the weight difference, woven fiber has some area pass across each other. So, woven fiber is heavier than UD fiber. But, for rims, the size of carbon fiber is not large and only one layer different, the weight difference of woven fiber (3k &12k) and UD fiber is not big. Also, all rims have a weight range, for rims, it is +/-15g. So, sometimes, 3k rims & frames are lighter than UD.
For big size product (like frame), 3k frame will be heavier than UD. And for 12k, the weight different is not much difference.
carbon rim weave 3k matte
carbon rim weave 12k matte
carbon rim weave UD matte