I agree. If he surprises his sceptics and scores a ton of goals between now and the end of the season United will want to keep him. However, instead of being able to get him for a fair fee Burnley will probably ask for two to three times that.
If Weghorst smashes it at Old Trafford he will want to stay, we will want him to stay and Burnley will know they can't keep him.
With two years left on his deal at the end of the season, Burnley will see sense in cashing in. However, I doubt the Burnley directors will want to let him go for the kind of cheap fee Besiktas had an option for. Burnley will probably point out how much we paid for Van Persie, when he was of a similar age and with a similar amount of time left on his Arsenal contract, and say inflation is much higher now than it was in 2012. It could get messy.