This is a meta-analysis of the risk factors for long covid (12+ weeks of symptoms) in the UK. They are looking at multiple longitudinal studies, where people are followed when they get covid to see how long symptoms last. They are also looking at UK electronic health records.
Although women are less likely to have severe covid in the acute phase of the illness, they are about 50% more likely to have long covid.
People who were generally in poor health before getting covid were at higher risk for long covid, although the amount varies between studies.
Being overweight/obese increases risk of long covid by about 20-30%.
Asthma increases risk of long covid by about 30-50%.
The longitudinal studies found an increase in the risk of long covid with increasing age, with rates below 5% in 20-year-olds, about 10% in the mid-to-late 30s, and 15% in the early 50s.
The electronic health records showed a peak in middle-age, with highest rates from 40 to 60.
We actually don't have any data at all about the reduction in risk of long covid after vaccination. But the vaccines reduce risk of infection, and if you don't get infected at all, you can't get long covid. I would guess that long covid is less common in vaccine breakthrough cases, due to the lower viral loads. But I'm sure it does still happen in some people.
Link to study:
https://www.medrxiv.org/content/10.1101/2021.06.24.21259277v1.full.pdf