• Overweight and obesity are factors in migraine but the link is not fully understood. 
• Studies have shown that whilst obesity does not cause migraine it can contribute to an increased frequency of attacks and also may make attacks more severe. 
• A clinical study discussed in an article published by the National Institute of Health in America (1.) suggests that obese patients were three times more likely to suffer migraine than a matched population. Also obese patients are more likely to have increased frequency and severity of attacks. Obesity also increases the risk of someone with an episodic pattern of attacks developing a chronic pattern.
• The relationship between obesity and migraine may be due to the inflammatory nature of fat. Fat causes low level inflammation in the body and also affects hormone levels associated with migraine. 
• Obesity also causes vascular changes, sleep apnoea and insulin resistance which are all factors in worsening migraine.
• Achieving or maintaining a healthy weight is certainly a valid goal for migraine suffers as it has such an impact on quality of life.​

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2974024/