It's often understated how vastly disproportionate the population of Roman and Allied Italy was compared to the Carthaginians. Our best source for this is Polybius' histories.

According to Polybius, at the start of the Second Punic War, Rome had a potential pool of 700,000 Infantry and 70,000 Cavalry that it could levy among its own citizens, colonists, and allies within Italy. Even still, the Romans rarely did not mobilize the entirety of its manpower pool, rarely mustering above 240,000 men for the course of the entire war. These individuals were still part of the war effort through their economic activities. Additionally, most crops and trades were taken over by soldiers' relatives, such as the women of their family or elderly men past fighting age.

By contrast, according to Polybius, Hannibal had at most 20,000 infantry when he crossed the Alps into Italy, with an additional 40-60,000 dispersed throughout its empire in Spain and North Africa.

Thus, while key battles at the River Trebia, Lake Trasimene, and Cannae saw massive amounts of casualties for the Romans, the sheer manpower pool of the Republic allowed it to keep chugging along, albeit with great difficulty. Towards the end of the Second Punic War, the Romans were forced to draft adolescents, the elderly, and even slaves, into its armies.

However, purely as a level of demography, the Romans had a clear advantage. Although demographics of both Italy and Carthage are sketchy, the Roman census records from Augustus' era (14 CE), give us an idea of the population imbalance.

The core of ancient Carthage is based around modern Tunisia and coastal Algeria, with some minor colonies across Hispania and Morocco. Most of these colonies were sparsely populated, with less than 30,000 to 50,000 residents at most. By comparison, Carthage was the core of their Empire. Based on the work done by 19th Century German Historian Karl Julius Beloch, we can estimate the population of ancient Tunisia/Carthage at around 1.4 Million in 14 CE. By contrast, ancient Italy had a population of 7.0 million at the same time.

Carthage also had a much different social structure, with the majority of citizens only rarely staffing military units. Instead, much of the fighting was done by mercenaries paid by Carthage's extreme wealth and fortune. This was a critical weakness, since Carthage needed to maintain both its wealth and good relations with its neighbors to recruit soldiers into its armies. This includes Celts and Spaniards in its colonies, as well as Numidians and Libyans in North Africa. This weakness was made known during both Punic Wars, as well as the Mercenary War that occurred during the two wars.

By contrast, the Roman military was staffed by its own citizens who were called up to war, and were augmented by their Socii Allies and allied tribes. This allowed the Romans to rely on loyal, and motivated troops, who were both more numerous, more disciplined, and more motivated that the Carthaginians to conduct its war effort.

This imbalance was key to understanding Hannibal's strategy for the Second Punic War. Most of Hannibal's men were professional soldiers, or mercenaries, not levies. Because of this, they did not need to disband to return to their fields and tend their crops. Instead, they were supported by plunder and the wages paid by the Carthaginian state. This allowed him to operate for years in enemy territory. However, this came at a cost of not having a steady supply of troops, and being consistently outnumbered by the Romans and their Italian Allies. Hence, Hannibal's strategy relied on attempted overtures to Rome's Italian allies to rebel and side with Carthage. However, because of Rome's resilience, and the strong political and diplomatic connections with its allies, this was an ineffective strategy.

Works Cited

Brunt, P. A. (1971): Italian Manpower

Frier, Bruce W. "Demography", in Alan K. Bowman, Peter Garnsey, and Dominic Rathbone, eds., The Cambridge Ancient History XI: The High Empire, A.D. 70–192, (Cambridge: Cambridge University Press, 2000), 827–54.

Goldsworthy, A. (2000): Roman Warfare

It's of my opinion that Roman Senate under the leadership of the Dictator Quintus Fabius Maximus made Roman citizenship more flexible in order to not only bolster the Legions of much-needed recruitment but to also fill in gaps their economy allowing them to take paid jobs that allowed them to pay taxes. I would assume this to be offered to un annexed regions of the Republic such as colonized Cities where the natives were the majority.