Do you eat back your exercise calories and lose weight?

If 500 isn't really causing 1 lb weekly on avg over a month of time - then it's not because of exercise calories that it could be pinned on.

It's somewhere between logging what you eat being accurate.
Logging what you do being accurate. That's daily activity and exercise.

I've always lost eating back exercise calories. Your deficit is still there to cause weight loss - why wouldn't it?
Exercise is for body improvements - and if it can't be good hard workouts - I'm not getting improvements from it.
If I didn't eat back workout calories - my workouts would suck.
Waste of time then - merely burning a few calories.

Age may have you with less muscle mass then you used to have - especially for people that have yo-yo dieted with extreme deficits frequently.
Age also has people moving less daily, outside of exercise.

So it's not that 500 deficit won't cause 1 lb weekly loss over time - it's the values to determine that are off.

The difficult thing with not logging and eating back exercise - you have no basis for your calories then.
When it comes time to adjust or figure out where the problem is - no info.

Hiking and a long walk would be a low calorie burn activity, and the way MFP handles adding those calories 50% is best method.
Running 75% would probably be right.

Any issues to not seeing the deficit could be daily activity is below sedentary - for many it is now.
Or food logging issues. Logging by weight, right, not volume?

And your deficit so far could be stressing the body, that increases cortisol, that increases water weight.
That can slowly increase while fat weight is dropping. Always do measurements too, scale is not a 1 best measurement device.
Of course body stressed like that not good.

1/2 lb weekly would be reasonable for 15 lbs to lose - but that takes accurate food & exercise logging, and then adjusting after a month of results of adhering well.

I'm 64, 5'5", been using MFP quite consistently since 2015. I started at just over the line into a class 1 obese bodyweight (183 pounds), lost down to mid-150s in about 4 months by ballpark-estimating calorie intake, then joined MFP to start counting more formally. I was 59 at the time.

When I joined MFP, I started estimating exercise calories (carefully) and ate pretty much all of those calories back in addition to my base calorie goal. In about another 7 months, I was in the 120s, and working to settle into maintenance calories. So, a little under a year to lose about 50 pounds +/-.

I've been maintaining up and down a bit since, mostly 120s/130s - at 127.2 this morning. I've been eating exercise calories back throughout. (I'd point out that in weight maintenance, it's essential to account for exercise energy expenditures somehow, or loss will continue beyond goal weight! In retrospect, it was helpful to me in maintenance that I had experience doing that during weight loss - didn't need to develop it as a new skill after hitting goal.)

I've been very active for a long time, well over a decade before this weight loss effort, even while obese, so the exercise routine was not new during weight loss. Until the pandemic, my routine had for the last few years been spin classes 2 days a week all year long, 4 other days on-water rowing in season, and a bit lighter schedule in the offseason of machine rowing, mixing it up with maybe a little swimming, sometimes strength training, etc. Since I have that seasonal variation, and because my summer exercise is weather dependent, the separate accounting for exercise calories works very well for me.

If it matters (I think it doesn't), I'm also severely hypothyroid, but properly medicated.

Sometimes while losing, and pretty much always now, I bank some calories (eat a little under goal) in order to eat a bit more indulgently occasionally. Those aren't explicitly exercise calories: I get there these days by setting my base goal 150 calories or so under my estimated actual maintenance needs, and eat to that level plus that day's exercise calories, generally. (Might bank slightly more calories for a couple of days in advance if I have a special event coming up soon, or something.)

IMO, what heybales said is exactly right, throughout.

That said, no calculator or fitness tracker tells you what your calorie needs or calorie deficit are, exactly. They just give you estimates, as a starting point. Assuming you're tracking calorie intake consistently accurately - a refinable skill in itself! - then your actual average weight loss rate over a period of weeks, plus the amount you ate over the same period, tells you what your calorie needs are (at current habits/routine) and implicitly tells you what your actual deficit is. (You want 4-6 weeks of consistent data at least, whole menstrual cycles if premenopausal so you can compare weights at the same relative point in the different cycles.)

BTW, MFP doesn't really suggest calories: It's an output from a formula for which you set the inputs, including your self-assessed average activity level (which should *not* include intentional exercise if you plan to log it separately, as MFP is designed for), and your targeted weight loss rate (which would sensibly be 0.5 pounds/week if you only have 10 pounds to lose). A problem is that with a weight loss rate that slow: It's hard to see on the scale through the noise of daily water weight and digestive contents fluctuations in anything less than a couple of months - as I know because I've been intentionally drifting my weight downward for the last few months at about a pound a month rate. For pretty much the month of July, even the trend line in my weight trending app looked like I was gaining because of water weight changes when I resumed strength training, but the ongoing slow fat loss showed up eventually.

Bottom line, after that long explanation: I've been eating my exercise calories back 100%, after estimating them carefully, through months of weight loss and several years of maintenance. Personally, I think exercise calories taste the best.😉😆

I'm about the same age and height as you and find that if I set MFP to lose weight at 1 lb/wk and eat back exercise calories I usually lose about that if I am good about logging and measuring. So many things at play. I also find that the more intense the exercise, this helps to kick my metabolism into high gear, so I do at least 3 days a week of some interval and/or heart rate training while trying to keep my heart rate at around 130. I also try and fit in 3-4 days of strength training, as muscle tends to burn more calories at rest. My understanding is that our bodies when eating in a deficit for too long may slow our metabolism, so this could cause issues as well.

While it is different for each of us, you just have to find out what works best for you.