How does being overweight compromise the immune system for instance whe it comes to breast cancer reoccurence?

Estrogen levels : About 80% of breast cancers are estrogen receptor positive ie they are stimulated to grow by estrogen in your body . After menopause when the ovaries stop producing estrogen the levels fall significantly but not to zero . Low levels of estrogen are made in fat tissue and if this is a larger amount this can be relevant in increasing the chance of the cancer recurring.

Unclear: This is unclear, but we do know that being obese increases your risk of developing several different types of cancer. Maintaining a healthy weight will reduce this risks.