With the help of friends who are familiar with civil aviation and relevant laws and regulations on flight cancellation, can airlines cancel flights at will because of "weather reasons"?

Airlines are generally reluctant to cancel flights, but some special reasons can cancel them. What you said does exist. For example, when there is wind and rain, large aircraft, such as A380 747-400, may not meet the landing conditions. On the contrary, small and medium-sized planes can land. Sometimes large aircraft can take off and land, but small and medium-sized aircraft can't, depending on the weather parameters. Airlines may also be unable to deploy the appropriate aircraft to complete the mission due to capacity reasons, so they may cancel. You can see if there are similar planes arriving at the same time.