Why was Jeroboam able to field twice as many soldiers as Abijah?

Jeroboam fielded 800,000 soldiers because the northern kingdom consisted of ten Israelite tribes, whereas Abijah's southern kingdom of Judah and Benjamin had only two tribes. That numerical advantage in tribes and population allowed the north to raise twice the troops.

In 2 Chronicles chapter 13, Abijah of the southern kingdom of Judah and Benjamin could raise only 400,000 chosen men of war, while Jeroboam, the first king of the northern kingdom, set 800,000 men against him. Les explains this is logical because the northern kingdom had ten tribes and the southern kingdom had only two. As history continued, the numbers reversed: the northern kingdom could later field only 580,000, while the southern kingdom came with 1,160,000. Les teaches this happened because of a mass migration of Israelites out of the northern kingdom down into the southern kingdom over the years.

2 Chronicles 13:3

And Abijah set the battle in array with an army of valiant men of war, even four hundred thousand chosen men: Jeroboam also set the battle in array against him with eight hundred thousand chosen men, being mighty men of valour.

How did the military strength of the northern and southern kingdoms compare later in history?

Initially the northern kingdom fielded 800,000 troops against the southern kingdom's 400,000. Later in history, the northern kingdom could only muster 580,000 while the southern kingdom brought 1,160,000, reversing the earlier advantage. This shift resulted from a mass migration of Israelites from the northern to the southern kingdom.