Why doesn't font family change take effect when using AtBeginEnvironment{figure} together with memoir?

The memoir class provides its own hooks for floats:

\setfloatadjustment{figure}{\sffamily\tiny}

In general to invoke <code> at the beginning of every <floatname>, add the following to your preamble:

\setfloatadjustment{<floatname>}{<code>}