There's also something to be said about sentimental value if you're that type of guy. I have a Model 7 in 308win that took me a long time to save up for years ago. Since I had it I've killed 18+ deer with it along with a ton of squirrel using cast loads. That rifle fed my growing family during our hardest years. I always had a pressure issue with the barrel though. Now that I'm a riflesmith, after finishing up a project I decided to pull the barrel on my trusty Model 7. Low and behold Remington chambered it with a cant. Yes, a cant... Not only that but the chamber was generously large. It's a wonder it shot at all!
With a wide range of reamers at my disposal the only thing I could justify turning the rifle into.... was a 308win. It just seemed right. She started that way. Served me well. And will finish that way. Except this time I'll chamber it with zero runout and perfect headspace.
If you decide to keep your dad's rifle as a 300 Weatherby you'll never feel like you did wrong by it or him. It served him well and it will serve you well if not for anything, but the memories.