Type II Diabetes has a lot to do with genetics and not only what you eat. My doctor was (female) 5'6" and weighs 115. At her heaviest she weighed 120. Very physically fit, jogs every day and works at the gym 3 days a week. So yes, because your father is Type II, you could be headed down that path. A heavy person is more susceptable and can bring it out sooner in life. By staying trim and fit, you have a better chance, but it doesn't mean that it's not going to happen.
Carbs are in most everything you eat and you should be careful with carbs. There are good carbs and bad carbs. Some carbs can be processed by your body more easily than other carbs. Good rule of thumb is white food is a no no. White Flour, sugar are good examples. Anytime you can keep carbs in check, it's better, but you are still going to encounter carbs. Most white bread is 22 carbs or higher, where as the cracked wheat bread I buy is only 14 carbs.
Now add to that that people are different on how each individual processes carbs. One person can eat pasta and not have a problem and the next person can eat pasta and their Blood Sugar goes through the roof. One person can eat pasta and their system processes it in 3 hours and the next person takes 6 or 7 hours to process.
So Diabetes is NOT an exact science that works on every individual, every time. All you can do is do what you can.
I've found that keeping a journal of every bite of food I eat has been very beneficial. I have to test my blood sugar 4 times a day. At the end of the week I go through my journal/spreadsheet and look at readings that were higher than normal. Some of them can be attributed to a particular item and, there for, can be avoided, but I've found that some combinations can cause higher than normal readings. I can eat a particular item and my body handles it just fine, but if I eat it with another item, the two can cause me to have higher than normal readings.
Because Type II runs in your family, now is the time to start paying closer attention to it. I would recommend that you pick up a meter and test yourself once a week while fasting. Say every Thursday morning, before you have anything to eat or drink, you test your blood sugar. This could give you a heads up so that you can discuss it with your doctor and get a head start on it. Remeber the old saying, an ounce of prevention......