Is it true that the average weather of an area over long periods of time is weather?

No, the average weather of an area over long periods of time is climate. Weather happens from day to day and from year to year. Climate change takes longer than that. So the fact that 2010 was warmer than 2011 means only that weather changes from year to year. There are spikes, both up and down, in measurements and we have to look at longer term averages to see trends.