What your mother said

Biblical records describe how Tiglath-Pileser III exacted 1,000 talents of silver as tribute from King Menahem of the Kingdom of Israel (2 Kings 15:19) and later defeated his successor Pekah (2 Kings 15:29).

Pekah had allied with Rezin, king of the Arameans against Ahaz (known to the Assyrians as Yahu-khazi), of the Kingdom of Judah, who responded by appealing for the Assyrian monarch's help with the Temple gold and silver. Tiglath-Pileser answered swiftly. He first marched his army down the eastern Mediterranean coast, taking coastal cities all the way to Egypt. This cut off his enemies' access to the sea. Once this was achieved, he returned to the Northern Kingdom of Israel, destroyed their army, and deported the Reubenites, Gadites, and the people of Manasseh to Halah, Habor, Hara, and the Gozan river (1 Chron 5:26). He then installed an Israelite puppet king, Hoshea, (732–723 BCE) in the place of Pekah. He concluded this extensive campaign by marching north and west, ravaging Aramaea, seizing Damascus, executing Rezin, and deporting the survivors to Kir (2 Kings 16:9).

Beyond this, the Assyrian alliance was not beneficial to Ahaz (2 Chron 28:20).