> enters into essential matters for the well-being of society.
Which has poorly defined boundaries because people disagree on essential.
In practice "Big Government" is used only for PR value. It sometimes seems the more a politician or policy wonk uses it, the more they are actually likely to increase government spending when they are in power.
Most people seem to use "Big Government" to mean they don't like something the government is supporting or regulating, and "Essential Government Function" to mean something they want the government to pay for or regulate.