Why did Georgia and the other states favor a weak central government under the Articles of Confederation?

The answer is:

Georgia's first constitutional convention met and produced the state's inaugural constitution, known as the Constitution of 1777. Several other states also chose the convention method as a means of adopting new constitutions

There were some issues regarding these different methods like the legitimacy of the constitution-making process

Explanation:

The government they established was a confederation, a loose organization of states where the power remained in the individual states with the central government remaining weak. The government was composed of a Confederation Congress with limited powers. It had no executive or judicial branches and no power to tax or to regulate trade.

State law was supreme, problems with war debts, trade, and diplomacy spurred many of the new country's leaders to call for a revision of the Articles of Confederation to give the central government more power to deal with these problems.