From what I have researched a big belly is stress belly or inflammation belly. I have that problem too. Somebody can have very slim legs and a massive tummy still which makes one look like a fat heifer. Often it is the incogruence of it which looks worse if there was just fat all over.
So, it is the slim waist that matters really, more than any other part of the body (and also good posture!) The ways to shrink the bloated fat stomach are essentially to do with reducing stress in any form and reducing gut inflammation. The former include meditation, good quality restful sleep, yoga and relaxation practices, dealing with anxiety, worry etc. Stress accumulates over time, so a 40 y.o. will be more stressed than a 20 y.o. just by the virtue of living through more stressful experiences, them all building up.
Weightloss is blocked by cortisol which increases appetite and drives us towards rich carby foods for quickly accessible energy. It also affects sleep. So as much as it sounds wishy-washy, lowering cortisol levels and increasing well-being will result in weight loss.
Gut inflammation is caused by consuming poor quality processed food, e.g. deep fried, high in sugar, wheat for a lot of people/dairy.
I found when I eat low carb, my tummy is slimmer and a lot less bloated than when I eat ‘normally’, with bread, grains, potatoes, pulses. My gut seems to react to these foods which results in bloating, discomfort and generally bigger waistline.