What causes the "imperialism of economics" and how did it start? Wikipedia defines "economics imperialism" as follows:


  Economics imperialism (often economic imperialism) in contemporary economics refers to economic analysis of seemingly non-economic aspects of life, such as crime, law, the family, prejudice, tastes, irrational behavior, politics, sociology, culture, religion, war, science, and research. Related usage of the term predates recent decades.


My question is this. What is it about economics as a discipline that has allowed the it to extend to these "seemingly non-economics aspects of life?" Also, when did economic analysis in these so-called unrelated fields become accepted as part of mainstream economics?
I find the following quotes to be interesting:


  "[Political economy is] a branch of the science of a statesman or legislator [with the objective to provide] a plentiful revenue or subsistence for the people [and] to supply the state or commonwealth with a revenue for the publick services."—Adam Smith, 1776.
  
  "Economics is a study of man in the ordinary business of life. It enquires how he gets his income and how he uses it. Thus, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man." —Alfred Marshall, 1890.
  
  "Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses" —Lionel Robbins, 1932.


Together, I think these quotes nicely illustrate the way that economists' perceptions of their own discipline evolved over time. By the 1930s, we have Robbins' startlingly insightful observation that Economics is about choice subject to constraints, which is obviously a very general kind of problem. But even as early as the late 19th century you can already see traces of this kind of thinking in Marshall's words.

This way of thinking about economics is, I think, key to emboldening economists to reach out beyond the confines of market behavior. Indeed, I think one reason why economics has been so imperialistic is that economics is as much a methodology as a body of knowledge. As such, economists have constantly looked for new problems and settings to which they can apply the tools they know.

More recent contributions that have been important are probably:


The work of Gary Becker, whose Nobel citation reads "for having extended the domain of microeconomic analysis to a wide range of human behaviour and interaction, including non-market behavior" Those non-market behaviors include important things such as fertility, marriage, and crime—not traditionally within the domain of economics.
The development of game theory and information economics. These tools equipped people with new ways of modelling social environments. A classical supply/demand type model, or a general equilibrium framework will get you quite far when studying traditional markets, but these tools are much less suitable for studying non-market behaviors that are the preserve of economic imperialism. New modelling frameworks brought about by game theory, the principal-agent model, etc. really opened the way for studying all kinds of new environments.
The Downs model, which was an early application of economic-style (specifically, Hoteling's linear city) modelling to political science—one of the most thoroughly 'colonized' disciplines.