i have always considered the Bridge Doctor a weapon of last resort. There are a number of reasons for tops to distort, broken/cracked bridge plates and loose braces being two of the most common. Addressing those issues should be first. I realize that sometimes Bridge Doctors are necessary, but in the case of the guitar you are looking at, gluing the loose brace and verifying the condition of the bridge plate may result in no longer needing a Bridge Doctor.
Note that if a bridge plate is cracked/broken, it can be an expensive and non-trivial to dangerous repair. I am not saying that this guitar has a broken/cracked bridge plate, just bringing up possibilities. In contrast, re-gluing a loose brace is probably the most common repair on an acoustic guitar, and very safe.
In general, adding weight to the top of a guitar will be detrimental. How detrimental is very dependent on the particular guitar (top stiffness and weight, bracing, etc.). Hand builders go to great lengths to minimize top weight (including thickness, bridge material (rosewood/ebony) ) and optimize stiffness, so hanging a 4-5 oz. weight (or whatever a Bridge Doctor weighs) cannot possibly do any good for tone, or more accurately, will cause the top to be less optimally balanced for tone. Factories do the same, just not to the same degree, but the Bridge Doctor will have the same effect, just not as pronounced.