Dissolve removes the boundaries between features based on the attributes, there is no builtin way to constrain it further with a 'sum to within' option. In fact adjacency checks for attributes are generally quite difficult. This would be further complicated, if not impossible, if there were not gaps in the geometry, since dissolving on an attribute which appears in all polygons would effectively produce a large continuous polygon.
Perhaps an image of what you have might be useful. In the interim, you could try selecting polygons below some threshold value, then aggregate those to larger units through dissolve.
