The hardest part of walking for a stiff back is the reason. Photography supplies one: a walk with a camera is an outing with a purpose, and the purpose is what gets the miles done.
Does carrying camera kit count as exercise?
Carrying is load, and load is what bones and backs respond to, for good and ill. A light kit on a short walk is useful weight-bearing movement; a tripod and full bag on a moor is a different proposition entirely.
The photographers who work British hills think about this seriously. The site landscape photography kit notes on Slant Light cover tripods on peat and scree, filters held against hill wind, and how to carry the minimum that does the job.
How do you walk further without noticing?
By having something to stop for. A walker who stops for light on water walks further than one counting steps, because the pauses are the point rather than an interruption. The pauses are also when a back resets.
Ordnance Survey maps and routes, at ordnancesurvey.co.uk, give the walk a shape before you leave the house.
What is the lightest useful kit?
A camera and one lens, or a phone. Everything else, tripod, filters, spare lenses, is a choice about load, and the choice should be honest: if the bag is too heavy to carry happily, it stays home, and so do you.
When does the walk outweigh the photograph?
On the day the light is wrong. A walk taken for a photograph that never appears is still a walk, which is the whole trick of the thing.
For the movement itself, the benefits of stretching every day pair well with the miles.