Exercise makes a big difference to weight - not just because exercising a lot makes you lose it, but also because if you're into cardio exercise, generally you'll want to be lighter so you can move more quickly and be better at the sport that you do.
I am talking about proper, hard, regular exercise rather than the odd reluctant gym class or an infrequent walk with the dog though...
There are countless running studies that demonstrate the relationship between weight loss and speed. I've also seen it myself. After losing a stone, running became far easier and that was reflected in my PBs.
But for a simple visual example, go to any 10k race.
From my pretty extensive experience, any of the women finishing in under 40mins (ie very serious runners) will be very lean indeed, with barely any extra flab.
The vast majority of the women finishing in under 50 mins (lots of training required) will be slim.
Between 50 and 60 mins (average time for runners of all abilities) the women will be anything from slim to average, with the odd overweight person here and there.
And any woman finishing in over 60 mins (first timers, usually) will be any shape and size at all, because generally they're not yet running hard and frequently enough for it to have made a massive difference, or they haven't been doing it that long.
Ok, it's not scientific - but there's a reason there's virtually no successful runners, cyclists etc that are overweight. That's because they train hard, eat well and don't live the sort of lifestyle where a trip to town means a gallon of creamy coffee, a cinema visit means a vat of popcorn and a family day out means McDonald's.
There's also a reason why the average size of people gathered at a 10k race is generally far less than the average size of the same number of people at a cinema or in a shopping centre.
People have such a warped idea of what "normal" exercise levels are that they say "I'm fat and fit" - yet their version of fit is being able to walk on the flat for a couple of hours, or make it through a step class once a week. They're kidding themselves.