What authority given to congress has been most instrumental in expanding its power relative to the other branches of government?

The answer is "taxation and appropriation".

An appropriation bill is a bill that puts cash aside for particular spending and in many vote based systems, endorsement of the law making body is essential for the administration to spend this money.In the United States, these bills for central government spending are passed by Congress. The fiscal year of government keeps running from October 1 through September 30 of each schedule year and each year, the president presents a spending proposition to Congress. 
Taxation is a method by which governments fund their consumption by forcing charges on natives and corporate substances. Governments utilize tax assessment to energize or debilitate certain monetary choices.