How did the Constitution help with weak government in 1783?

First, to clarify, the Constitutional Convention would not meet until 1787. When it was ratified, however, it changed a great deal about the weak government under the Articles. The Constitution created three branches of government whereas the Articles mainly had one--the legislature. Under the Constitution the three branches of government each had checks against each other and no one branch could become all-powerful. The most important part of the Constitution was that it gave the federal government the power to tax. This was perhaps the most important as the government under the Articles could only request money from the states. This was plausible during the American Revolution though there were times when the Continental Army went without pay and supplies. The states banded together to fight Britain but after their common enemy was defeated each state looked out for its own interests. Many states only wanted to pay what they saw as their fair share of the national debt. By taking over the national debt and giving Congress the power to tax, the Constitution gave the United States the central authority it needed to manage a new nation of diverse interests.
The Executive Branch wielded new power under the Constitution. Though Washington set most of the precedents for the job, the position did have explicit duties in the Constitution. The Executive was to be Commander-in-Chief of the armed forces and he was to enforce the laws ratified by Congress. This gave the United States a centralized authority figure whom the rest of the world could claim was the leader of the American people.
By creating a centralized government, the Constitution created a system of laws that was stronger than the Articles of Confederation but was still responsive to the needs of the people.