Yeah this is pretty simple. So if you have a group of people randomized into two groups and you want to see changes in mean weight loss and one group lost 4 kg and the other lost 6kg, you will need a lot of people to show the 2kg difference was due to the intervention and not random chance. And if you had another experiment and group 1 lost 4kg and group 2 lost 40kg, you might not need as many people to prove these two values are different not due to chance.

In addition, sample size is used in the denominators of most standard error calculations. So this means the more people you have the more confidence you have in the effect estimate being close to the true value in samples. So in other words those whiskers on point estimates get narrower and are less likely to overlap between groups with different estimate values.