Hi,
Most people don't have power meters and do just fine. I use a Garmin GPS (without a power meter) to keep track of my rides, but a smart phone, or just entering the route and time by hand afterwards is good enough.
As far as weight loss goes, remember, the simple idea is that if you burn as many calories as you eat, you stay at the same weight. If you bike more and eat the same, you'll probably lose weight. Note that it isn't really that simple because the more you bike, the more you want to eat.
If you are close(ish) to your ideal weight, adding exercise is often sufficient. If it isn't, then it is worth going to talk to somebody about not only how much you are eating, but also what you are are eating. The kicker is that in order to lose weight, you really have to change how you eat. And if you lose the weight you want and switch back to whatever you were doing before, you'll probably put the weight back on. The good news is that if you make several small and manageable changes e.g., stop eating potato chips as your snack and switch to green beans), you'll be more likely to keep it up for, well, forever. And, yes, biking can be a big help here, too.
Cheers,
Charles