I can't say I know anything about a narrow throat. I imagine it could be because of excess fat or skin.
So you lose weight and your skin inside your throat becomes more floppy. That sounds plausible. I think that it becomes more important to exercise then.
Regardless of that, the studies have been done that show sleep apnea is reduced when you lose weight, exercise regularly and/or do the throat exercises.
Weight loss:
https://www.ncbi.nlm.nih.gov/m/pubmed/11122588/
Quote from study:
"RESULTS: Relative to stable weight, a 10% weight gain predicted an approximate 32% (95% confidence interval [CI], 20%-45%) increase in the AHI. A 10% weight loss predicted a 26% (95% CI, 18%-34%) decrease in the AHI."
General/cardio exercise:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4216726
Quote from study:
"The effect of exercise training on our primary outcome, AHI, was assessed by using two approaches. First, the pre-to postintervention analysis of five studies (six cohorts) showed a pooled estimate of mean change in AHI of −6.27 events/h (95 % CI −8.54 to −3.99; p < 0.001) with an I2=0% (Fig. 2), which reflected a 32 % reduction in AHI from baseline."
Tongue/throat exercise.
https://academic.oup.com/sleep/article/38/5/669/2416863
Quote from study:
"Current literature demonstrates that myofunctional therapy decreases AHI by approximately 50% in adults and 62% in children. Lowest oxygen saturation, snoring, and sleepiness outcomes improve in adults. Myofunctional therapy could serve as an adjunct to other OSA treatments."
Using weight loss, general exercise, and tongue/throat exercises I managed to get my AHI down to approx 5.
Not using a machine currently.