What is the criterion for aiding in sin, and does paying the internet bill or maintaining it for someone who uses it for unlawful purposes fall under this, especially since this person may not pay the bill himself, and the internet may be cut off from the questioner if he does not pay it?

If it is confirmed that your brother is using the internet for forbidden things, then you must advise him, enjoin good upon him, and forbid evil from him, to the best of your ability. If he does not respond, then no sin falls upon you, because you cannot prevent him, and you have fulfilled your duty. Your renewal of the subscription or maintenance is not considered assisting him in the forbidden, for the intention is to assist yourself and your family in permissible uses. There is no harm in assisting a disobedient person in a matter that is unrelated to his disobedience.