Cohesion and Coupling
Metrics focused on cohesion and coupling should give a good indication that your classes are real as opposed to collections of functions. There's a very readable paper here which I quote below to indicate why I think cohesion is a good metric:
"Cohesion refers to the relatedness" of module components. A highly cohesive component is one with one basic function. It should be difficult to split a cohesive component. Cohesion can be classified using an ordinal scale that ranges from the least desirable category (coincidental cohesion) to the most desirable (functional cohesion)."
The classic measurement of cohesion is Chidamber and Kemerer's "Lack of Cohesion in Methods" (LCOM). You can also look at Response for a Class (RFC) which measures the linkage between methods in a class.
You could consider design metrics such as NOC and DIT but my own experience is that they are too crude and easily confused by classes within a third-party framework.
You haven't said which language you use but there are some tools built around Eclipse so a quick web search for Eclipse based object oriented metrics should yield something useful