Is itt true the more you weigh......

the faster you lose. (with the same exercises as someone smaller)

Sure, because its requiring more effort of your body to do the same thing, so you burn more.

When I wore my bodybugg at 255 lbs, I could get in 3000 calorie burn days easily. Now, at 168, I have to REALLY work for 2200 or so.

There's one way to find out....

Yes and no.

For example, if you run a mile, you burn about 100 net calories. This is true pretty  much no matter how much you weigh. That's because, if you weigh more, you tend to go slower. So you aren't working as hard even if you think you are. It all kind of comes out in the wash with running.

Walking is the same. (Except it burns about 50 net calories)

Both have been studied a lot and this hold true across many studies.

OTOH, the every day tasks definitely take more energy and so your BMR is higher. That's how many calories it takes to make your body work even if all you do is stay in bed all day. So just existing burns more calorie!