How much eggplant is 3-4 pieces? I have an eggplant 3x the size of another, both the same type!

In my opinion, a reasonably sized burger patty (prior to cooking) is about a third of a pound, thus 5.3 ounces or 151 grams.

Working backwards, you'd probably want about 120 grams of mashed eggplant per patty. Combined with the other ingredients, this should get you very close to a 150 g patty.

Since this recipe makes 3 servings, you are shooting for 360 grams (or so) of mashed eggplant. Since peeling a vegetable like an eggplant typically results in 15% loss, I'd probably cook slightly less than a pound (~420 grams) of whole eggplant.

Best of luck.

Many if not most recipes for eggplant burgers unfortunately only give main ingredient as part of an eggplant, without saying weight or size.
One, thankfully, uses about 3 cups of combined beans and chopped eggplant for 4 servings.
Proportionally that's about 2c vegetable matter for the 3 servings here.
Or, estimate visually the first time you make the recipe how much you need for 3 servings, adjust as needed, keep notes on weight or volume used.