During the constitution convention, small states did not want their representation based on

 Small states did not want their representation based on SIZE OF POPULATION.

During the United States Constitutional Convention in 1787, the "Great Compromise" resolved the different desires between small states vs. large states.  The large population states wanted representation in Congress to be based on a state's population size.  The smaller states feared this would lead to unchecked dominance by the big states; they wanted all states to receive the same amount of representation.  The Great Compromise created a bicameral (two-chamber) legislature.  Representation in the House of Representatives would be based on population.  In the Senate, all states would have the same amount of representation, by two Senators.

the authority to tax.