If a human body is exposed to plastic fumes then definitely it will cause cancer. Now your concern is whether black plastic that is burnt underneath small rocks cause cancer. As long as it is giving out fumes, yes, it is very likely that cancer can be caused. Dioxins are by-products of plastics when burnt which are very harmful and toxic. These dioxins not only pollute air but also can pollute soil and crops which are grown. They not only cause cancer but also result in emphysema, birth defects in newborn babies and damage the immune system in the body. Dioxins have a rock-solid chemical stability. This is because they cannot be dissolved in fats and when they enter atmosphere or a body, they remain there forever.
People who are exposed to burnt plastic fumes are at higher risk for suffering from cancer. In these fumes, endocrine-disrupting chemicals are found and these chemicals help in the growth of cancer cells in the body. Carbon monoxide and furans are the other toxic chemicals which get released when plastic is burnt. All are carcinogenic in nature.
Kindly do not burn plastic. If you want to get rid of unwanted plants then there are many methods to do so including hand plucking or using some mechanical tools for the same purpose.
Plastic cannot be burnt. Most of the plastic melts and bubbles. I mean the open fire is not enough to burn all the toxic chemicals present in the plastic. The fumes pollute the air and will remain in there forever. Even the ashes so left can cause water pollution and enter the food chain. Some plastics are safe to burn but identifying which one is safe and which isn't is very difficult and thus to be on safer side, it is best to avoid burning them and throwing them here and there and better subject them to recycling.