When we walked (last half of August through the end of September), it seemed very busy in places and not so busy in others. This was our first Camino, so I have no way to compare it to other times of the year.
Regarding crowds, it seemed quite busy between SJPP and Pamplona, and of course the last 100 km, after Sarria. We took it slow, averaging just under 12 miles (20 km) per day, so we generally arrived at our place for the night in the early afternoon and never had problems finding beds. After Sarria, however, we did call ahead to private albergues to ensure that we had beds, but we only called the night before when we had a pretty good idea of our next day's destination. For the rest of the Camino, we just stopped where we felt like it and never felt the need to reserve ahead.
Weather-wise, we miraculously escaped the rain until we actually reached Santiago. There were a couple of foggy, misty days in Galicia, and one day along the Meseta where we had a very light sprinkle. And there was one terrific thunderstorm the night we stayed in Villarmentero, but it didn't start until we already in bed for the night and the sky was clear in the morning. Other than that, it only started raining on us as we were actually with Santiago and continued off and on for the four days we stayed there. The hottest daytime temperatures we experiences were a few days in the low to mid 90's F in late August/early September. The lowest were in the mid-40's F, primarily when we were at higher elevations. Be aware, however, that we walked during an unusual weather pattern, so more rain than we experienced would be the norm.
Hope this helps, and Buen Camino!
Jim