there are a whole lot of variables. That is the reason that when you see a description in a field guide, or other document describing a snake, the length is generally more specific than the girth. For length you will see an average range, ie; 48" to 52" (or expressed in metric units) and sometimes a record length. The girth is always more vague, such as "a heavy bodied snake" or "a slender snake". To some degree, snakes are individuals like people, and some will be heavier than others, especially in the wild. Snakes in captivity tend to be more on the obese side than they do in the wild. They will grow to a certain length, partially dependent on available food and partially due to the genetic blueprint for that species and age, then essentially stop growing. I say essentially because most will continue to grow at some rate all of their lives. The growth rate is very fast in the first couple of years of life, then slowing more and more as the snake gets older, during the last few years of life it will be nearly imperceptible.
Girth, for many species, is more dependent on food availability than genetics. For other species, especially those that are naturally more slender (especially active arboreal species), and have higher metabolic rates, girth seems more dependent on genetics. They don't seem to get particularly fat even in captivity. I've never seen (that I can recall) a really obese Mamba. Other more sedentary arboreals, such as Green Tree Pythons, can become obese in captivity.