Can aerostats be used for fine-grained control of the weather Most of the discussed geoengineering ideas aim to change the average temperature of the earth instead of trying to control local weather.

Aerostats can be used to change the local temperature in several ways:


if covered with reflective material they can create shadow;
if covered with dark material they can significantly increase the temperature above the cloud potentially dispersing the cloud;
if combined into a structure similar to a solar updraft tower, they can transport dust and humidity to the height where they would not be transported by natural winds and by that either condensate the water or create new clouds.


With a large enough number of devices like this it should be possible to guide humid air to deserts, or to prevent hurricanes by removing convective available potential energy on their path.

Is there any research about the possibility of controlling the weather with devices like these, or is there some obvious flaw that would make this completely impossible? (Lack of helium is not a good argument, as these aerostats are not meant to lift any additional weight, and are meant to be as large as possible, so could use air heated by the sun).

If this is possible, what percentage of earth surface would we need to cover with these devices to counteract CO2 effects? From a rough assessment of incoming radiation vs radiation trapped by human released CO2 it seems to be much smaller than 1%.
No, the idea is quite impractical. Lack of helium is no obstacle because unmanned balloons, whether tethered or remote controlled could be filled with hydrogen, but to affect the climate you would need millions of them, which is too expensive and impractical. Geo-engineering projects are generally the stuff of science fiction and not practical in the real world. One way climate could be modified on a local scale is to refill places like the dried up Aral Sea with water from the ocean. Apart from other beneficial effects, this would probably produce enough evaporation to affect local rainfall. Rainfall is also locally affected by the presence or absence of trees, so if you want to increase rainfall in arid areas, one way to achieve it is large scale tree planting. That might be difficult in semi-desert environments, but nevertheless it has been done. Sometimes tree roots can reach down to a water table, which is how enormous cypress trees are in some places  able to grow in the sand seas of the Sahara Desert.