does skipping breakfast make you gain weight?

Normally yes - 90% of overweight people skip breakfast. Why - it makes them hungry later and eating later when the demands for energy are over causes the body to store the energy from a late meal in fat instead of using it on activity. The body has to regulate how much glucose is in the blood and the glucose comes from digestion. When excess glucose is available the body must convert it into something else and store it for future use. Especially is this true when a person eats less than 3 hours before going to bed. The food being still in the stomach keeps the person from restful sleep - and makes them feel tired and lethargic when they get up. However the stomach is tired and wants a rest becasue it had to work when they were trying to sleep. So the stomach says don't feed me breakfast - And they don't feel as alert as they would if they had had a good nights sleep without their sleep being disturbed by digestion. So the cycle begins and encourages people to be overweight.

I've been skipping breakfast for years. If I do eat breakfast I am more hungry through the day and have to eat more than normal. I like to fast leangains 16 hour fast/8 hour eating window. Benefits of intermittent fasting include weight loss.

"Generally speaking, intermittent fasting will make you eat fewer meals.

Unless if you compensate by eating much more during the other meals, you will end up taking in fewer calories.

Additionally, intermittent fasting enhances hormone function to facilitate weight loss.

Lower insulin levels, higher growth hormone levels and increased amounts of norepinephrine (noradrenaline) all increase the breakdown of body fat and facilitate its use for energy.

For this reason, short-term fasting actually increases your metabolic rate by 3.6-14%, helping you burn even more calories (10, 11)."

10 Evidence-Based Health Benefits of Intermittent Fasting:
https://www.healthline.com/nutrition/10-health-benefits-of-intermittent-fasting

No!! quite the opposite.
Consuming carbs/sugar laden cereals does. eg; Toast, jam, cereals, orange juice etc
Eating eggs/bacon, avocado, mushrooms etc is the best start to the day as these foods are not carbs and do not raise your insulin....Insulin is what makes you gain weight.

Breakfast is the most meal of the day skipping is a bad idea.

It sort of depends on what happens the rest of the day. For some people who skip breakfast, when they get to their first coffee break they are really hungry and end up snacking. Maybe on two donuts. so a bowl of oatmeal for breakfast would have been a better idea.

I'm not that hungry in the morning and so what I usually do is skip breakfast and have an early lunch. then I have an early dinner. It works out well for me unless I stay up late and get hungry and have a nightime snack.

No, it doesn't

No it doesn't.
I haven't eaten breakfast for many years now, for a long time I only ate once a day (early evening) but now I occasionally eat a snack or two if I am going for a long cycle ride 30 km or more.
I am 72 years old, slim, fit and super-active, so it hasn't done me any harm.
Humans aren't built for 3 regular meals, we spent hundreds of thousands of years as hunter/gatherers which usually meant eating our catch around the fireside late afternoon/evening (assuming we were successful) it is the life evolution designed us for,
Which is why with our modern way of eating there is so much obesity.
Look at the primitive tribes in the Kalahari and other places, you wont find any of them being fat.

Skipping meals, particularly breakfast, lowers your metabolism so you gain weight or fail to lose weight at a lower intake level than someone with a higher metabolism.

Eating too irregularly and having sudden peaks of glycemia/insulin can promote fat gain, but it depends on the context and it's typically a weak effect. What really matters for fat gains is whether there's a calorie excess in total on the whole day. Some people do "intermittent fasting" while being careful about the daily total and eventually they look rather healthy.

Another thing is that skipping breakfast will lower muscular protein synthesis and put you in a long catabolic phase, so that you will typically end up being less muscular. Having less muscles can also indirectly make you fatter, since muscles consume a lot of calories.

And a third point is that skipping breakfast makes you very inefficient during your morning, so it will reduce your NEAT, i.e. you will burn less calories than if you were able to stay more active physically and mentally.

Finally, skipping breakfast is usually correlated to taking less care about your nutrition, and this could bias the correlations that we observe from an epidemiological point of view. Because those correlations do exist, see for instance http://jandonline.org/article/S0002-8223%2805%2900151-3/abstract "Breakfast eaters generally consumed more daily calories yet were less likely to be overweight" or http://www.jahonline.org/article/S1054-139X%2806%2900264-3/abstract "Fast food consumption and breakfast skipping increased during the transition to adulthood, and both dietary behaviors are associated with increased weight gain "

is this showing?