Pressure & temperature

I'm confused about what determines the local altimeter setting. My
understanding is that there is a barometer in the tower that measures
the weight of a column air extending up into the atmosphere. What
factors affect its weight? Is it purely temperature variations caused
by uneven heating by the Sun or is there something else?

In a similar vein, I understand that winds are caused by pressure
discrepancies which lead to winds moving from high to low pressure
areas. Again, are the pressure differences caused by temperature only?

Thanks.