Firstly I'm a female, and my DH is supportive of my efforts, he in fact was the first one to lose a bunch of weight in our house, unfortunately during that time I was pregnant and not on board with him (nor did I want to be). And let me just say it is really hard and sort of threatening to be married to "one of those guys", you know the ones that eat right all the time and workout every day. And that is especially true if you're not on board with all that "healthy lifestyle" business.
Okay you say she is "fit and beautiful", but as a woman I can tell you that most of us do not feel confident in our own appearances, no matter what we look like we can always find a dozen things to hate. What we see when we look in the mirror is a little chub here and some flab there and holy crap look at those crow feet
! So let me ask you, have you told her lately that she's beautiful? Or that you love her? Or that she's the hottest thing on God's green earth? Seriously a little demonstration of your affections can go very long way towards smoothing over the rough patch that a lifestyle change can cause in your relationship. It might also do to remind her that an in-shape healthy husband is way more fun, more vigorous (in the bedroom especially) and romantic than a blah couch potato husband.
I can also say that when I first started doing all this it was my usual "New Year's resolution", so DH didn't pay any attention to it. But once I'd hit the 40lb mark he added another workout at the gym to his weekly routine. So the longer you do this, the more accepting of it she'll be, so just give it some time to sink in.