Yes changes in weather and barometric pressure can affect arthritis.
When the barometric pressure changes it can cause your muscles, scar tissue and tendons to expand and contract which can cause your joints to swell up and cause pain from arthritis.
When the barometric pressure changes and it gets cold my Grandma always complains that her joint pain from arthritis got worse.
I always thought she was just complaining but now that I have arthritis myself I also notice the pain of the arthritis increases in my joints when it gets colder.
Then when the weather warms up again the arthritis pain gets better.
So yes barometric pressure does have an effect on arthritis due to the swelling and expanding and contraction of your joints caused by the barometric pressure changes.