Do you know when is the right time to buy very fat crabs to be eaten?

Male crabs usually have more meat than female crabs. Also crabs which have just moulted will have less meat (by weight) than crabs which are about to moult. There are so many different kinds of crab that it is impossible to generalise but there are certain signs which tell you when a crab is about to moult. When a crab has recently moulted, the shell will be soft, gradually hardening over several hours. The new shell will also contain less meat in proportion to its total weight, so, if you buy crabs by weight or by the bushel, make sure that the shells are hard and that the crab shows signs of being ready to moult. This page: http://www.serc.si.edu/education/resources/bluecrab/molting.aspx shows the stages of moult in a blue crab but other crabs may be different. The answer is to know your crab! There seems to be NO hard evidence that the phases of the moon affect moulting and crab size. It is much more likely that water temperature and the availability of food have the largest influence on both the amount of meat and the moulting cycle. Crab meat contains hardly any cholesterol (fat), so crabs can never really be described as 'fat'. In general, crab meat is very nutritious but you should be aware that, like most crustaceans and shellfish, crabs can store high levels of toxic substances, especially heavy metals. Also, they go "off" very quickly once they die, so they should always be bought live, if possible, and cooked very soon after buying.

Crabs are delicious. Especially the fats ones, but eating a crabs are sometimes difficult and messy. Still, its delicious even their shell is hard to break.

That's true during days without moon the crabs are fat and is very good for them to buy an opposite of the sea urchin wherein during full moon the content is full.