Interesting question. There is some correlation between weather changes and mood and anxiety, but there are too few studies to answer this question convincingly. From this highly cited study, rising barometric pressure was associated with increased concentration, decreased sleepiness, and increased feeling of control. So rising barometric pressure is associated with improved concentration, alertness, and confidence. There was no correlation between barometric pressure and anxiety.
With regards to other weather variables, anxiety increased when it was raining or snowing, but anxiety decreased when sunshine hours increased and the temperature increased. Concentration decreased with increased humidity. Sleepiness increased with rising temperature and humidity, but sleepiness declined with increasing barometric pressure. Aggression increased with decreasing temperature. Scepticism decreased with increased hours of sunshine and higher temperatures. And optimism increased with increasing hours of sunshine.