Weather ≠ Climate we are told, time and time again.
In fact Climate is an average of weather recordings over time:
Climate ≈ Weather/Time
Or more correctly:
Weather/Time → Climate as Time → ∞
(Weather over time tends to climate as time tends to infinity).
However time is continuous. So this means that weather over time in short periods does indicate short climate states, however inaccurate in comparison to longer time periods. This suggests that the original proposition is a misrepresentation.
Climate ≈ Weather for small time, would be a better statement.