What should I do if the cat is very weak?

If the cat has been stuck for some considerable time and is now weak, you need to make some provision to fetch the cat down. Ask around the neighbors to see if anyone has a ladder or is skilled at climbing trees. Alternatively, contact an animal welfare organization who may be able to put you in touch with someone with the necessary equipment. Also, think laterally and phone a local builder or roofer, and ask if they are an animal lover. You could suggest you'll contact the local media station, who may be interested in such a story and cover it, providing free advertising for the business in the process.