During the second Punic War it was pretty clear that Hannibal could subjugate Rome. From the Trebia River and Lake Trasimene to the famed Battle of Cannae Hannibal routed Roman army after Roman army after Roman army on a shoe string budget and established himself as basically uncontestable to the Romans, they could not defeat him. But due to Hannibal's lack of full fledged support from Carthage all he could do was just slap the Roman legions around northern Italy, he could never really establish any annexed territory and firmly insert his foot into Roman ass. Why didn't the Carthaginian government back continued involvement in the Italian peninsula? Given all of Hannibal's success it seems like Italy would have belonged to Carthage if they had wanted it.
it was pretty clear that Hannibal could subjugate Rome
That's a bold statement and not one I'd agree with. Hannibal had some quick successes with three decisive victories in battles, but winning a war is a different story (as Maharbal famously quipped: "You, Hannibal, know how to gain a victory; you do not know how to use it." (Livy XXII.51)). While among Hellenistic states it was common for a state to sue for peace after losing a battle, Rome always refused to do so. Pyrrhus was the first Hellenistic commander to figure that out (to his own detriment) well over half a century before Hannibal. The Roman gears of war grind slowly but steadily.
The only way for Hannibal to defeat Rome would be to take it by force. However he lacked siege equipment to take Rome by direct assault and investing Rome was infeasible given the size of Hannibal's army and the fact that Rome's closest allies had remained loyal.
The cities which did defect to Hannibal were all in southern Italy, with Capua being the most important defector (in 216 B.C., after Cannae). These cities expected Hannibal to protect them, which forced Hannibal to stick to that area. No longer could he do his quick and long marches which were so advantageous to him in the first couple of years.
Rome meanwhile had learned their lesson. They stopped trying to fight Hannibal directly and turned their attention to the cities instead, protecting those which remained loyal and threatening those which defected. In 211 Rome recaptured Capua and punished it severely. No cities defected to Hannibal after that.
While Hannibal was mucking about in southern Italy, Rome's slow and steady approach was working for them. They had armies in Sicily and Spain, attacking Carthaginian (and allied) strongholds directly. In 212 B.C. Syracuse was besieged and taken by the Romans, giving them nearly complete control over Sicily. In Spain the brothers Publius and Gnaeus Scipio had mixed success before they were killed in battle in 211. Publius' son was sent to Spain to take command of the armies and continue the war. He was hugely successful and within two years had taken New Carthage, Carthage's main stronghold in Spain.
Carthage itself meanwhile was in a bind. They were facing losses in their own territories while Hannibal had some prime troops holed up somewhere where they couldn't offer help, nor could they threaten Rome (Hannibal tried to threaten Rome in 211 B.C. in an attempt to lift the siege of Capua, but he failed.) Carthage did send Hannibal a few reinforcements in 215. More reinforcements were planned, but they were diverted to Spain to fend off the Scipiones. This shows that the Roman strategy was working.
In short, Carthage "didn't truly back Hannibal" because Hannibal wasn't in that good a position and because they had their own territory to defend. Eventually Hannibal was called back to Africa to defend the city of Carthage itself, as Rome had taken over all other Carthaginian territory while Hannibal was 'winning' in southern Italy.