Glad you asked. First of all, fat (adipose) tissue and muscle tissue are two completely different types of body tissue, and they increase or decrease in size via entirely different processes.
Excess fat accumulates when calorie intake is more than what the body needs to support bodily functions and physical activity. Extra calories are stored in the form of fat tissue. Fat loss occurs when calorie intake is less than what the body needs; in this case, it provides a reserve of energy the body can use as needed to make up for a negative caloric balance.
Muscle tissue grows (hypertrophy) in response to a challenging stimulus — like lifting weights. Muscle loss (atrophy) occurs when there isn’t enough of a stimulus to maintain its current level of size and strength; this happens when someone stops or cuts back on strength training, with bed rest, some disabilities, and aging.
To lose excess fat in your arms, you’ll need to lose excess weight all over your body; spot-reducing is a myth; it just doesn’t happen. Sadly, doing arm strength exercises doesn’t melt away arm fat. Sustainable weight loss involves improving your eating habits and reducing total daily calories consumed. It also involves regular physical activity, including both cardiovascular exercise and total-body strength training.
Be sure to check with your health care provider before starting a new exercise program. For best results, work with a registered dietitian for a personalized meal plan and healthy eating guidelines. A certified personal trainer can help you establish a safe and effective exercise program to help you meet your weight loss and fitness goals.
Enlarging your back muscles would require specific strength-training exercises targeting those muscles. But most men and women don’t have the genetics to develop excessively large muscles; a huge increase in muscle size is unlikely if you follow basic recommendations for strength training. Exercising your back muscles as a part of a balanced strength-training program offers many benefits, including injury prevention.
Rest assured that shaping up your arms with a weight-loss program and a standard cardiovascular and strength-training program isn’t going to bulk up your back.