The reports of his 2001 hospital stays as delivered and sourced by Le Figaro and CBS are evidence. They aren't proof, they may be wrong, but they are evidence.
So are these reports:
July 2, 2001: Osama bin Laden Periodically Undergoes Dialysis with Approval of the ISI
Indian sources claim that “bin Laden, who suffers from renal deficiency, has been periodically undergoing dialysis in a Peshawar military hospital with the knowledge and approval of the Inter-Services Intelligence (ISI), if not of
Musharraf himself.” (SAPRA (New Delhi), 7/2/2001) While one might question the bias of an Indian newspaper on this issue, highly respected intelligence newsletter Jane’s Intelligence Digest later reports the story, and adds, “None of (these details) will be unfamiliar to US intelligence operatives who have been compiling extensive reports on these alleged activities.” (Jane's Intelligence Digest, 9/20/2001) CBS will later report bin Laden had emergency medical care in Pakistan the day before 9/11. (CBS News, 1/28/2002) If these stories are true, it appears Pakistan could have captured bin Laden for the US at any time. The Jane’s Intelligence Digest article adds, “It is becoming clear that both the Taliban and al-Qaeda would have found it difficult to have continued functioning—including the latter group’s terrorist activities—without substantial aid and support from Islamabad (Pakistan).” (Jane's Intelligence Digest, 9/20/2001)
http://www.historycommons.org/context.jsp?item=a070201renal
Here's a collection of partly conflicting claims:
http://www.doctorzebra.com/prez/a_binladen.htm
Among others, Peter Bergen leans one way, Lawrence Wright another.
This claim cites a PBS Frontline hour and sounds like evidence to me:
"A journalist who visited bin Laden's camp in the 1990s reported camp members saying that bin Laden had a kidney problem requiring him to drink large amounts of water. The journalist witnessed bin Laden constantly sipping water and green tea in the time they spent together."