Weed free check treatment in weed control experiment is included to determine the weed index which indicates percent reduction in crop yield in different weed control treatments as compared to weed free check.
Weed index = (Yield in weed free check - Yield in other weed control treatment) x 100 / yield in weed free check
For statistical reasons. Check treatments, weed free and/or weedy, have to be included in order to be able to compare and contrast your weed control treatments with the extreme "good" or "bad". In your real life, everything could be relatively compared to something else in order to get a better idea as to what is considered "suitable" or "unsuitable".
Weed free check treatment in weed control experiment is necessary to evaluated the effects of treatments and of uncontrolled weeds on crop yield reduction.
If we want to check the weed index, weed control efficiency and herbicide control efficiency, we have to include weedy and weedfree checks along with other weed control treatments.
Weed free treatment is necessary to examine the effect of the herbicide, physical or mechanical weed control treatment on the economic crop in absent of the weeds. may be the herbicide have a stimulator or inhibitor effect on the crop.
I read the prevous answers. I want to add that by creating a weed free soil surface one generates a state susceptible to other yield limiting factors, such as soil erosion (weed cover can limit it efficiently in many situations). Therefore the observed differences in crop yields are not only due to weed competition, but a combination of yield limiting factors occurring successively along the yield build-up process from land preparation to harvest.
weed free check treatment is necesssory to to know per cent yield reduction in different treatments i.e. weed index. weed index is calculated by yield from weed free check plot - yield from treated plots/ yield in weed free check plots X 100.