Can aerostats be used for fine-grained control of the weather
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.