If the delay seems weather- or ATC-related, I would take a screenshot of the weather forecast/map and/or the FAA flight delays page for the departing/arriving airport (e.g., "traffic destined for JFK is on a ground hold due to WEATHER:TX SWAP with average delays of 2 hours 31 minutes and increasing"). You can try to submit that as documentation. I had a flight delayed from one evening until the following morning back in September when we had the remnants of a hurricane, and in submitting for reimbursement for the airport hotel to the Amex travel delay insurance, I actually included printouts of news articles about the storm and flooding. Don't think I had any other "proof" of the delay reason. Claim was processed with no issues. YMMV I guess.