http://www.collegedata.com has much of the common data set information. Under the “Academics” tab for each school’s entry is the class size information.
Note, however, that even if only a small percentage of classes are large, the fact that they are large means that a lot of students take them. For example, if a school has 100 students, each of whom takes two classes, and there is one 100 student class and ten 10 student classes. If each student is in the 100 student class and one of the 10 student classes, then each student will see an average class size of 55, which is much higher than the average class size of (10 * 10 + 1 * 100) / 11 = 18.2.