I did not read every word of the discussion/argument in this thread, but I gave it a good skim.
I'll chime in with a few comments.
1) At least anecdotally, it seems biking can absolutely be an effective part of a weight loss regimen. I say this because I have a friend who lost something like 80 or 100 pounds a few years ago and has kept the weight off. He tells me he did it by eating a little bit healthier diet (nothing extreme or really strict, just cutting back a bit) and by riding his bike a lot. Individual results, of course, will vary.
2) Keep in mind a well-proven principle of weight loss: to achieve it, you must exercise at an intensity that elevates your heart to around 70% of max, give or take, and sustain that level for at least 30 minutes (40 to 60 minutes is better).
I believe my friend when he tells me biking is almost exclusively to thank for his progress. And I still believe what doctors and researchers have been saying for decades about exercise intensity and duration.
To me, this means one must be pretty committed and have a reasonably convenient place to ride. Many people do. Many others are probably better served by a stationary bike, treadmill, lap pool, or some other exercise arrangement. Weather, traffic, terrain, and other factors can unfortunately squash the good intentions of someone who wants to use a bike for weight loss (or other fitness goals). Running, with its often-cited drawbacks (not least of which is potential for joint damage) allows for faster calorie burn and easier intensity regulation. By that I mean it's easier for a runner to adjust pace/effort to remain in the desired heart rate zone. Cyclists often have more trouble with this due to the factors I mentioned three sentences up. It is still my favored exercise method. I am not in need of weight loss, but I am trying to maintain my overall health and fitness, mostly by biking as often as practical.
Now, if we're talking about the morbidly obese, biking is probably not an option. That's okay, because they will start losing weight as soon as they cut back their diet and take daily walks for 5-10 minutes or whatever they can handle. Once they get below 300-ish pounds, biking might become viable. For those who are just moderately overweight, I say "Yeah, ride a bike!"