Is hypertension a consequence of being obese?

Not always. Although many people with hypertension are obese, there are also many people who are normal weight with hypertension. There is metabolic syndrome, which includes hypertension, pre diabetes, high cholesterol, and obesity, but hypertension can also be a consequence of obesity, eating too much salt (a minority of people with hypertension), or other causes.
Not exactly. Some people can be obese and not get high blood pressure. However, if you have a genetic predisposition (runs in the family) for hypertension then becoming overweight can make your blood pressure go up.