I have noticed that when I look at a cropped picture of someone's face, I fill in the remaining image of his/her body in a manner that is consistent with the face (wider face, larger body, skinnier face, frail body, large jaw, more muscular body, etc). Does the human brain immediately and accurately fill in such information and guess what a persons's body looks like from just images of the face?
Yes, barring weird instances of swelling that is localised to the face, for example. Evolutionary psychologists argue that facial cues, including adiposity and skin pigmentation, to name but two, serves as a cue for general health. If this argument holds true, it means that humans developed a fine-tuned ability to make quick judgments about someone's fitness to mate based on various factors related to health, of which facial features happens to be a big one. This might also explain why we find highly symmetrical faces more attractive, as facial symmetry is positively correlated with genetic health markers.
Another example is the seemingly robust correlation between testosterone levels and the square jaw that you mentioned. In turn, testosterone and muscle mass are linked. Ao seeing someone with a square jaw, you automatically infer their testosterone levels as well.
Apart from that, there is an obvious correlation between facial adiposity and BMI, which heavily influences judgments about general health and mating preference.
Short answer: You have this ability because it's highly advantageous when it comes to making judgments about choosing good mates.