Without knowing more detail about your metabolism than anyone without a medical degree could hope to comprehend, the only way to figure it out is keep walking further each day until you start losing weight. Back in my younger days (from ages 15 to 35), I had a high enough metabolism that I would burn off more calories sitting on the couch than many people did walking. I was only moderately active but required somewhere in the neighborhood of 4,000 calories a day just to maintain weight. Now that I’m in my forties, it’s a much different story and I’ve gone from 20 pounds underweight to about 30 pounds overweight without changing much about my lifestyle. Yes, metabolism matters!
Now that we’ve got that out of the way, in order to lose a pound a week, you pretty much need to drop about 3,500 calories a week or 500 calories a day. Your little walk, if done every day without altering your diet, is about half that. While it may seem long, 2.7 miles a day at a normal pace isn’t terribly much for someone who is going for weight loss unless they have some other exercise going on. Good for cardio, maintaining muscle tone, and for regaining use of injured legs, but not enough to actually drop pounds on it’s own.
However, walking with busted ribs sucks. Life in general sucks with busted ribs. So increasing your exercise probably isn’t really feasible for now, at least not to the degree required to achieve your goals just by walking. Until you are well enough to handle 7–10 miles a day, you’ll need to get that 500 calorie a day cut some other way.
Dropping 300 calories a day from your diet would work. Another thing that may help is biking. Unless you ride like me, it’s much lower impact than walking. Hell, on good roads/paths or using a stationary bike, it’s lower impact than rolling over in bed! As someone who has been through physical therapy a couple times and spent a couple months re-learning to walk without a cane I’m all about “low impact”, and with your ribs, biking may work well for you too. And biking at a relatively sedate 10 MPH burns about the same calories as leisurely swimming; both burn twice as many calories as a 3 MPH walk.
For reference, my buddy decided to lose a little weight and he’s dropped about 50 pounds in the last six months, but he generally walks at least five miles a day and when he’s in the mood to actually do some physical activity (about once or twice a week) he’ll get on his bike for another 30–60 miles. All that on top of watching his diet; weighing out portions, refusing to eat anything that lacks nutritional info, and all that.
I’m thinking walking alone won’t do it unless you get pretty hardcore; at least 10 miles a day at 3 mph. And if you’re taking in more than about 1,800 calories a day (subject to a little adjustment based on factors like age and height) then it will be that much harder and slower.