any advice on whether it's risky to fly edinburgh to heathrow with 3-hour window between arrival at heathrow and departure to u.s.?
If it's on one ticket then no problem.
If you've got separate itineraries then you're cutting it a bit fine.
You'll probably be coming in at Terminal 5 and departing from Terminal 2 never leaving the secure area. That said if your luggage is checked through you yourself will perhaps only have to clear a secondary security checkpoint for U.S. bound flights. I think 3 hours is OK unless you are catching a late afternoon flight (Heathrow is famous for backups and delayed landings/departures).