Holding a hand near the projection screen casts a well-defined shadow. Moving the hand back toward the projector makes the shadow indistinct: the edges are too fuzzy. Were thumb and forefinger creating a silhouette with a hole, it would become difficult to discern the hole.
There is a similar difference between dimming the sun from millions of miles away and doing it in the stratosphere close to the target.
Uniformity of aerosol application is difficult to accomplish—and maintain—via sun-scattering aerosols in the upper atmosphere. This means that the cooling will tend to be as patchy. What happens with patchy cooling from this aerosol silhouette?
Temperature differences create density differences—and thus winds are generated between the air column of the cooling silhouette and uncooled neighboring regions. At many altitudes, more dense air will flow sideways out of the silhouette column. A patchy silhouette could rearrange the generally eastward track of storm systems, though simulations are needed to estimate how sensitive the storm tracks are to this.
Weather disruption might be avoided by doing the uneven scattering at some distance toward the sun, though that does nothing for the shadowed nighttime side of the globe with its warmer nights. And even a uniform application, pole to pole, will create an ever-moving stirring along the terminator that is not the natural one.
There is, however, a circumstance where patchy cooling from stratospheric aerosols might be of use—say, for cooling a region with out-of-control forest fires. There is now a need to break up the blocking highs that stall eastbound weather systems to cause three-day downpours, prolonged heat waves, and facilitate the prolonged arctic outbreaks into the subtropics.