Here are some things that I’ve heard, but don’t have cites for, so take them with as many grains of salt as you’d like:
Private colleges charge higher tuition because they tend to be tuition-driven, as opposed to public colleges that can rely on tax money and research grants.
The biggest factor (so I’ve heard) leading to increasing tuition rates is the “need” to keep the facilities and technology current and modern: computer labs, smart classrooms, campus-wide internet access, up-to-date athletic facilities, etc. Campuses that don’t have these things will lose students to those that do.
One common strategy employed by private colleges is to set tuition rates high (thus getting as much money as possible from students whose families can afford it), while offering plenty of financial aid (scholarships, grants, etc.) to keep the actual price you pay within reach of plenty of others.