What weakened the land of the Israelites after the death of Solomon?

The split into two kingdoms.

Rehoboam's father, King Solomon, had levied relatively heavy taxes, which had been used for such large-scale endeavors as building the First Temple. The fact that the nation was so prosperous and happy in his time (1 Kings 4:20) demonstrates that Solomon conducted his governance in a praiseworthy manner.

After Solomon's death, the people approached his son Rehav'am (Rehoboam) and asked that he now lower the tax. He ignored the counsel of his elder advisers and refused the people's request. This led the Ten Tribes to turn away from him (1 Kings ch.12).

The background reason was because King Solomon had been less than perfectly righteous. This led God to punish him by diminishing his dynasty in the lifetime of his son (Rehoboam). 1 Kings ch.11.

A deeper reason is that God wanted the more righteous people of Judah to be influenced by the Ten Tribes as little as possible.

See also:

Solomon's errors

Jewish history timeline