What does a "weary room" mean? [duplicate]

It's an example of metonymy (more specifically, hypallage), where the property "weary", which logically and literally applies to the people in the room, is instead applied to the room itself.

So it means something like "room full of weary people", or possibly "room that makes me feel weary".

Wiktionary provides a general definition of reading the room, which involves perceiving the mood of the people in the room. It’s a common phrase in show business.

Entertainers (even speakers) often have someone who appears before them who “warms up the room.”

Cue Magazine, 1969 · ‎Snippet view · Miss Diller will again be appearing with Ward Donovan, and greater love hath no wife for a husband than to let that man "warm up" the room for her. Don Rickles, hot as a pistol in Las Vegas and everywhere else these nights, does a return two-week gig at the Copa Nov. 13-26. The other big sparklers belong to the Empire Room .

A weary room would be an unresponsive one.