I am 5.3" / 161cm and weigh 170lbs/77kg
You say you eat a healthy diet, but you don't say what it's composed of so we can't really help without details. You say you exercise, but don't say doing what and how much, so again, what you think is enough or healthy might not be. Consuming fat isn't the only factor in weight, and the type of fat you consume is key. You don't mention your HDL levels, but eating too little fat can be a problem too as beneficial fat is necessary for proper metabolism and energy. You're also very young, so any problems from being overweight aren't likely to manifest themselves yet. Cholesterol isn't a consensus choice for the main causes of heart disease -- there are many factors and different causes. It's great your cholesterol is in good levels and hopefully that's where they'll stay. By the way, overweight people do have a greater propensity for certain illnesses but they don't necessarily have worse overall health than other people -- that's another myth. Just because you read that it causes, say, Type 2 diabetes in some people doesn't mean they die any sooner than a thin person who doesn't have that problem but might have other problems. Life is more complicated than that, and much of what we hear is advertising, not balanced facts about overall life expectancy and health.
Have you had your thyroid hormone levels tested? Inability to lose weight is a very common symptom of hypothyroidism (under active thyroid). You can ask your doctor to test TSH, Free T4 and Free T3, along with thyroid antibodies to determine if you have the autoimmune condition called Hashimoto's Thyroiditis.
I was overweight and had the same thing. I did have insulin resistance causing weight gain but I didn't eat a lot of food (underate actually due to poor appetite). The food I did eat was sugary stuff but I do love my bacon, eggs and butter. :)
To add, the bacon, eggs and butter were not causing issues. The sugar was.