Jacques Louis David completed a large number of portraits during his career, mainly of established figures from the upper classes and aristocracy. He became an incredibly well connected artist who pushed himself to the front of the queue when significant commissions in France came about. He was also highly respected, technically, and gave us some of the finest portrait paintings to have been seen in the 18th and early 19th century. In some cases he would offer to paint close friends and colleagues but on other occasions he would be commissioned to focus on other figures. These could be rich noblemen, or perhaps their wives or children. One can imagine these paintings being hung in their respective family homes, which invariably would be a countryside mansion, on the outskirts of Paris.
The lady herself in this picture is dressed formally, though in a fairly comfortable posture. She sits up straight on a red velvet chair, with elements of wooden decoration just showing through behind her. Her dress is made of white cotton, perhaps fairly thick and heavy. She sports a small shawl over her left shoulder and elements of it then hang down below her leg, revealing a patterned tip. Her makeup is heavy on the cheeks, entirely appropriate for this period, and her hair is also in the classical style of that period. She looks fairly young, but confident too, and is no doubt from a high ranking family where opportunities for her still exist, even despite the difficulties for women in society at that time. Choosing to complete these portraits would not only earn the artist good levels of payment, but also help him to further establish his reputation and connections within the upper classes for future benefit.
Robertine and Anne-Marie-Louise were the Rilliet sisters who had married well and were now able to enjoy their privileged positions. Despite that, they did not wish to have their portraits to be too extravagant, wearing relatively simple but smart clothing which they would have felt best represented their own characters. To have been painted by such a famous artist would have been enough in itself, and no doubt both pieces would have been hung proudly within their homes for a number of years, long before they would become part of a major gallery's collection, as they are today.