The thing is that the Roman Republic was already dead from the murders of the Gracchi brothers (120 BC) or the Social war (90 BC) - by that time the Roman republic was an oligarchy with no control on the elites.
Marius followed by Sulla took advantage of this and were Emperors in all but name, as was Caesar.
In fact the “Emperors” for the first 300 years were titled “Princep” — “first Citizen” - hence the term used is the Princepate.
During that 300 years the Republic technically continued with lessening power, until Diocletian started the Dominiate and threw away the last fig-leaf of a republic.
I don’t see weather as a factor from 130 to 27 BC - rather that the Roman Republic became an Empire without an Emperor and didn’t know how to manage its new wealth.
Exactly, it was a system that was not prepared to outlive the attempts of its own wealthy and influential people gaming it.
1) Roman political institutions and traditions, designed for a city state, were unequal to governing a large empire.
2) Roman cultural concepts like "dignitas" where a Roman aristocrats sense of self worth and honor were intricately tied to their prominence and achievements.
3) Political leaders such as Marius, Sulla, and Caesar were therefore willing to become autocrats as the only way accomplish their goals. It wasn't enough for Rome to succeed, they had the be the ones responsible for that success.
Climate, was probably a condition that exacerbated the political/military/economic environment and provided obstacles and opportunities that otherwise would not have occurred.
That is all plausible, but it leaves unaddressed the point that weather calamaties and famines do have effects. My guess is that with modern science now providing proof of a cause, historians of ancient Rome will find proof of the effects.
Arrogance, greed, pride, over-expansion, improper planning to deal with over-expansion, nepotism, personnel gain over service/infighting, fear about
“heading for tomorrow” because of finance/civil troubles, cynicism over benevolence (More reaction though) etc... nothing new under the sun, human nature is a b’tch sometimes.
I think the death knell for the Republic came with Hannibal, much earlier. Italia had been a land of virtuous farmers until Hannibal laid waste to farms and fields all over the country, which were then bought up by the rich, who became powerful landowners with the massive import of slaves to work the land. The people, essentially, went on the government dole. Yes, the failure of the Grachii brothers to achieve reforms, the Social Wars, Sulla’s reign, all played their parts, but they were consequences of this fundamental shift toward a slave-driven and increasingly oligarchic society. We should take note, as well, that in the end, Statism and socialist, perhaps even what we could call communist efforts to save the economy of the Empire would prove disastrous.