It’s actually the opposite. In type II Diabetes, aka adult onset, it’s insulin resistance at the cellular level that makes for abnormally high blood glucose levels. So even when you have “normal” or high insulin levels, the blood sugars stay high. So the body then releases even more insulin, which then results in additional fat storage, which then worsens the cycle, as being more obese worsens insulin resistance.
Type I diabetes means your pancreas isn’t making enough insulin. These patients aren’t resistant to the benefits of insulin, they just need to replace what would be naturally occurring. They use far less insulin than the type 2 patients who get administer it.