One thing you could try is to make the circles semi-transparent, by setting the
fill-opacity attribute on the circles to a value between 0 and 1, say 0.5. That way, the points with many overlapping circles will appear darker. I used this approach in a map example
Migrant Deaths over Time. It's not perfect, though, because after a certain number of overlapping circles you can't tell if more are added.
Another approach would be to count the number of circles that overlap at a particular location, then draw a bigger circle representing all of them, sized proportionately to the count.