In chess, the Queen is a powerful figure and the King is fairly weak. Was this a form of social commentary, and if so, what were the circumstances of the time that would have led to this?

The short answer to your question is yes. I've touched on the history of the Queen in chess here, which you may find interesting.

As far as we know, the king has always moved one square in any direction, whether we're talking about Chaturanga (the precursor to chess and other strategy games like shogi), Shatranj (old chess practiced for many centuries in India), or Chess. The only major innovation in the king's movement is the act of castling, which has existed in its current form since at least the 16th century (see Ruy Lopez de Segura's book Libro de la invencion liberal y arte del juego del axedrez from 1561). You say the King is fairly weak, but on the attack it is stronger than all but a rook or a queen. Emanuel Lasker, who was World Champion for nearly 20 years, thought the king was about as strong as a knight plus a pawn (4 points).

Regarding the queen, in early iterations of chess there was no queen. In Chaturanga, there was a Mantri (minister) or Senapati (general), who could move diagonally one square. In Shatranj, this piece moved the same way but was called the ferz (which Russians call the queen to this day). This piece was renamed queen (regina) in Western Europe perhaps as early as the 10th century AD. But many cultures kept previous terms. In Arabic, the queen is still a Wazïr (vizier). The fact that Western Europe largely adopted "queen" as the appellation of this piece is indeed social commentary, though historians are not sure when this occurred. We think the piece's power was dramatically increased during the high to late Middle Ages, and that this change was first codified in Lucena's 1497 book Repetición de amores e arte de axedres con CL iuegos de partido (though some claim this work was plagiarized from earlier work). Afterward, Western Europe adopted this change in movement and the name Queen became fairly standard. The rest of the world adopted this movement, but many cultures kept (and keep) older names identifying this piece with a man.