I don't have the equipment to test your hypothesis, but I think I can test an easier one: running a mile a day in addition to doing 10K steps in a certain period of time around the neighborhood. Crude, but predictable.
Try doing your walking first thing in the morning before breakfast. Lot's of bodybuilders use this technique when they are cutting for a contest. It's also a popular method because unlike cardio, walking has almost no detrimental effect on weight-training later in the day. I'd love to hear your results after keeping track of this.
Buy a heart rate monitor, they are dirt cheap, or just learn to accurately take your pulse. Then ensure you get your heart rate up to a set level for a set period. Walking burns next to nothing, it's good for your body for loads of other reason, and it's great for getting mobile, but will have a nominal affect on your body weight.
You don't mention if you are tracking food, which seems to be a major metric to miss out. I simply track approx carbs, which I find insanely easy.
Lastly other cheap metrics you could track are body fat (callipers cost next to nothing) which is easy to measure ESP with a friend helping, you can also track maximum widths. So what it the biggest part of you arm, leg, stomach, chest, neck, etc. just tracking weight is misleading as you could be dropping fat and gaining small amounts of muscle from your increased mobility.
Personally, I do slowcarbs (like low carbs but with pulses and beans) while weighing myself daily and taking body size and body fat measurements once a week. I've lost 15kg like this and dropped from 19 to 12% bodyfat. To get that drop I did no additional exercise, though now I cycle daily.