Putter fitting to me is an enigmatic concept. For tour pros, or anyone with skill, sufficient eye-hand coordination, and practice, you should be able to perform with almost any putter. The stroke itself is, at extremes, only about 3 feet long.
The fitting can, I suppose, make up for some of the deficiencies in those areas. I would guess that with proper, focused practice, you can eventually train yourself to see the line exactly where the ball begins, and learn what your sight biases are with any putter. That's how Jack, Arnie, and guys before lasers learned how to putt extremely well. Edel tries to achieve the same result by matching the putter to the golfer, so that the putter lines up where we think it is.
Most of us don't have that level of skill and coordination, and don't practice enough to putt like a tour pro. So, if we can get a putter that eliminates our sight biases (i.e. naturally lines up on the exact lines we see standing over the ball) then you can improve without all that practice. And, if it works, why wouldn't a tour pro--whose livelihood depends on putting well--take advantage of it?
The weighting doesn't make much sense to me though. You have to practice feel and pace on the greens. Whether you're using a heavy putter or a light putter, you still have to train your body how hard to swing the club to achieve a specific pace on your putts. For some, "heavier" or "lighter" might feel more comfortable, but beyond that I think whatever weight you choose is irrelevant until you can turn that weight into a proper pace.
I'll add that I see a lot of really bad putting form out on the course. You have to get your eyes directly over the ball, for starters--that way the line you're looking down is the same line you're putting on. Most bad putters I see (and bad golfers) have the toe up in the air, and their eyes are over their toes rather than over the ball (so they're looking down a line parallel to the putting line, offset by a couple feet). That injects a perspective angle into the equation that is completely unnecessary. Then there's the simple act of setting up square, which few people do (except on tour, of course). Then there's ball position: front foot, back foot, middle, and everywhere in between. At a minimum ball position should always be the same, but ideally a few inches forward of center.
Putting is really pretty simple if you do those three things. And a "fitted" putter is only going to fix tiny percentages. It won't do anything about the huge flaws in setup that I see killing most folks on the greens.