Doctors put T2's on basal insulin first because it's easy for the patient (one shot a day), when the optimal first insulin treatment for T2s would be bolus insulin with the training to count carbs and make corrections.
If you feel you can handle estimating carb content of what you eat, and doing a simple division calculation to determine an insulin dose, discuss dropping all oral meds and other injectibles except metformin, and starting a bolus insulin regimen with a fast-acting like Humalog, Novolog, or Apidra.
If you're willing to be an early user of a new insulin drug, Afrezza, that would be ideal (see several discussion here on TuD about it).
With your numbers and current treatment, it's near-certain that your pancreas can handle your basal needs on its own. So, in fact, you don't really need a basal insulin -- that was just an "easy" way to get extra insulin into your system so that between meals your BG would eventually drop to normal before you ate again.
However, with this approach you always risk hypoglycemia if you skip a meal, exercise and then eat too late, etc. This is an indication that the "basal" insulin you're taking is doing more than just covering your basal needs.
It's a bigger, more active commitment than the approach your doctor is taking, but it can make your control MUCH better, resulting in you feeling better, having more energy and being more active.
As far as the weight issue goes, while insulin does bias the body to convert carbs to fatty acids, it's really a second-order effect... Weight issues are first and foremost a caloric issue. It really is as simple as burn more than you take in each day, and you'll lose weight. However, like anything, data is king: If you carefully account for nutritional quantities and calories in all the food you eat, and manage your diet based on this, you will lose weight -- regardless of what you eat, and what insulin you put into your body.
So, all that said: Switching to a bolus insulin regimen (administration at mealtime, and during fasting when BG is too high and needs to be brought down), metformin (assuming healthy liver), and a suitable moderate/low carb diet with appropriate calorie content (calories are from carb, protein, and fat), and you can make this work.
Exercise: How about swimming?