How can the weather affect rheumatism, arthritis and lumbago?

Probably does not. Although it is commonly believed that arthritis is worse in damp and cold weather, studies have not really confirmed this. At best, the relationship is pretty weak.
Generally, musculo- Skeletal pain is related to soft tissue inflamation which can equate to soft tissue swelling. A low pressure system places less barometric pressure on rhe body and vice versa leading to the body acting like a barometer to predict weather.