Should I be concerned about it when my mother and grandmother have diabetes?

Diabetes mellitus type 2 (insulin resistance)  in first degree relatives would classify you as having increased risk for developing diabetes. This means that periodic (at least annual) screening with glucose testing and HbA1c measurement are indicated. Diet and exercise are the best strategy for prevention. 

Diabetes mellitus type 1 (insulin dependent) in a first degree relative is much less likely to suggest that you are at risk for diabetes.  It usually is associated with antibodies against insulin-producing cells in the pancreas.