The Great Compromise did not really involve the people who wanted a strong national government. Both of the sides in the Great Compromise wanted a strong national government. The Great Compromise was a compromise between the small states and the large states. The only way that we can say that it advanced the interests of the people who wanted a strong federal government is if we say that it made it more likely that the Constitution would be ratified by the states.
The Great Compromise was a compromise between the large states and the small states. The large states wanted both houses of Congress to be apportioned based on population. The small states thought that was unfair and wanted every state to have equal representation in Congress. The Great Compromise split the difference, apportioning the House of Representatives by population and giving each state equal representation in the Senate. This compromise had nothing to do with how strong the federal government would be.
However, the Great Compromise did do some good for the people who wanted a strong federal government. The compromise satisfied the big and the small states. This made it more likely that they would all vote for the Constitution. If the Constitution was ratified, a stronger national government would be created. Thus, the Great Compromise helped make sure that the Constitution would be ratified, thus ensuring that the US would have a stronger national government than it had under the Articles of Confederation.
In terms of how the Great Compromise supported a stronger national government, it did so because the bicameral legislature it set up is an integral part (and the law-making part) of the federal government. However, the issue of the Great Compromise did not so much hinge on issues of federalism (support for a strong national government) versus states; rights. Instead, the issue had to do more with how representation in the national government would be figured and what would be best for a fair representation. States with smaller populations wanted there to be an equal number of representatives for every state. However, states with large populations felt that this was unfair and felt that they deserved more representation because a higher percentage of the country resided in their borders. As such, the Great Compromise led to the system we have today, with the bicameral legislature split up into the Senate (where the number of representatives is equal for every state) and the House of Representatives (where the number of representatives is dependent on the population of the state).