I know that breast cancer in men is rare, but do men with manboobs have a higher rate of breast cancer than men with no manboobs?

Unproven. Men can have prominent breast tissue due to obesity (lipomastia) or a condition where there is increased glandular tissue--gynecomastia. It is often stated that gynecomastia is associated with increased risks of breast cancer, but no study has ever proven this. We do know, however, that high estrogen states can increase the risk of breast cancer in men (or women) and can be a cause of gynecomastia.
No. The size does not have anything to do with the risk for developing cancer.

Related Questions

What do lumps in the chest mean? Gynecomastia or breast cancer?

Either one + others. Most palpable female breast lumps are caused by either normal fibroglandular tissues, fibrocystic change, cysts, fibroadenomata, lipomas, focal mastitis (infection), or cancer. Gynecomastia by definition is male breast enlargement, usually from benign causes. It may be unilateral or more frequently bilateral. However, the are several thousand male breast cancers diagnosed each year.
Either. Masses in the chest could be gynecomastia or breast cancer. Best to be evaluated by your physician for diagnosis and treatment recommendations.

I am a 26 year old male and I have a lump in my breast. Can it be breast cancer or gynecomastia?

Breast lump. Gynecomastia is common in infancy, adolescence, and in middle-aged to older adult males. Pseudogynecomastia is also common and related to the heavy weight. Gynecomastia must be differentiated from breast carcinoma, which is far less common. There are a lot of cause of gynecomastia including drug, puberty, endocrine problems, liver/kidney problems etc. See your doctor and have your self checked.
Gynecomastia. Probably gynecomastia. But a biopsy with review by a pathologist would help solidify the diagnosis.
Find out. A lump in the male breast is usually breast tissue and is then called gynecomastia. The vast majority of these lumps are benign or non-cancerous. Rarely a lump could be a cancer so have it examined by your physician.
Breast Lump Dx. Best way to tell is by a mammogram and biopsy (needle vs open) see a plastic surgeon or general surgeon for consultation.