I would define "big government" as one that is overly intrusive in the day to day lives of it citizens or provides no benefit for the people despite massive costs.

-This is hard to quantify because the data is obscure and not something that can be observed based on a single number. For example, government declaring smoking or bubblegum illegal so you can keep your streets clean seems like an example of big government. Paradoxically, a lot of countries that have these sorts of policies tend to spend a smaller percentage of their GDP on government. Singapore only spends about 11% of its GDP on government programs, compared to the US 38%.

-The problem with big government is that it stems private growth or provides unfair advantages to specific individuals, or discourages diversification in policy.

A government that spends large amounts of money on its military despite having no credible threats drains energy and resources from the economy that could have been used to benefit industry.

In the US we have a problem with lobbyists that is basically legal corruption. A large company can pay for a politician's campaign, essentially guaranteeing they will win in exchange for their political support. This has a tendency to curtail the rights of individuals, and has been a critical factor in the radicalization of American politics.

America is very diverse. A government program that promotes science and technology may be good for the country as a whole, but has little benefit in the agricultural Midwest where schools must give up agricultural programs so they can adopt science related ones in order to maximize government funding. Many argue that things such as this would be better handled on an local level where the people are more knowledgeable of what is best for the community.

-Finding an ideal "small government" society maintains elusive because of all the factors to consider, and the fact that there can be no objective standard by which to measure. The index of economic freedom seems like a good indicator at first glance, but it doesn't consider government intrusion onto the lives of daily lives of citizens. It's about the centralization of power and authority, which is in contrast to the decentralization of power to the people.

By big government I think they are talking about the US federal government and complaining that it has grown far beyond its intended scope and purpose and has run up massive debts. Under the guise of regulating interstate commerce the federal government, for example, requires that lawn mowers and other implements be so equipped with safety features as to render them almost useless. The federal government has managed to intrude itself into the regulation of every facet of life—education, sports, food, health care and just about everything else. I’m sure that when those original thirteen colonies formed a federation and wrote a constitution they had no intention that the federation of states be all encompassing. Through taxation the federation controls most of the public money. They will “give” some of that money back to locals through various programs, but only if the local governments submit to stringent regulations and red tape.

It is like the EU. The members of the EU have no desire to have their local affairs micromanaged by the EU, thus you have Brexit. Imagine that in two hundred years the EU has grown in power to the point that it controls German factories, German schools, German farms, etc. that would be big government, with Germany being not much more than a province.