Please ask this question: When you have two facilities nearby and their service area overlap and you choose non-overlapping, what should happen to the overlap area? Should one facility get edges that are closer to another or should they be split such that each facility gets those edges that are closest to it?
Service areas are "grown" outward to the specified distance. When you specify non-overlapping, then the overlap areas can only be assigned to one of the facilities. By definition, edges are assigned to their closest facility. When an edge is equidistant to two facilities then the resulting service area will split the line at the place where it is equidistant to the two facilities.
So back to your case, if you have a facility with 7000 meter break surrounded by a number of facilities with 3000 meter break, the 7000 meter break facility is not going to get more edges assigned to it IF those edges happen to be closer to other facilities. So in your attached picture, other facilities "crowd out" your facility with larger break value as that is the solution to the non-overlapping case.
If you want to "preserve" a 7000 meter around a facility then I suggest you solve that facility separately, then use the resulting polygon as a barrier polygon in another service area layer loaded with other facilities and solve. Combine the results.
Jay Sandhu