In nearly all modern Romance languages, the future tense is constructed with "infinitive + habeo" (present of habere), and in most of them, the conditional tense is constructed with "infinitive + habebam", e.g. ES querer + había = querría and FR vouloir + avait = voudrait. But in Italian the conditional suffix is like habui (ebbi) instead of habebam (avevo), so the inflected word is volere + ebbe = vorrebbe instead of volere + aveva = vorreva. Is there a story behind this difference?
This story is way more complicated than I expected when I started researching it, and in fact explaining this particularity requires a fair amount of study of second/third century Latin, as well as some unbridled speculation.
It shouldn't have come as a surprise that the conditional mood, by far the most radical innovation of Romance, would have a very complicated history, but it was still exceedingly hard to find good references. So buckle up, we're going in.
1. Periphrastic constructions in late Latin
In late Latin, there were two periphrastic constructions that were muscling in in the subjunctive's turf: they were constructed using the infinitive followed (or sometimes preceded) by the imperfect and the perfect of the verb habĕo respectively. Since they seem to both cover roles corresponding to the Romance conditional, I'll call them the habebam-conditional and the habui-conditional respectively.
These two periphrastic constructions were not, however, synonymous. Unfortunately no grammarian has left us a detailed explanation of the difference in meaning, so we are left to try to suss out the difference from example of contemporary usage. Here I will present a very condensed description of the situation, based on the excellent detailed treatment in [1, Sec XXV.2].
The basic distinction between the habebam-conditional and the habui-conditional can be summarized as follows: the habebam-conditional denotes potentiality or predestination, where a situation could happen (or is even destined to happen), even if it hadn't happened yet, while the habui-conditional is used often to denote counterfactual situations, where the premise could never happen.
To this semantic distinction it is important to also add a morphologic one: the habebam-conditional seems to have been turned in a synthetic construction much earlier than the habui-conditional. That is, it is much more common to find examples where the infinitive and the verb habĕre are separated by an intervening word in the case of the habui-conditional.
I should also mention that it is possible to find occasional examples where the habebam-conditional is used where we would expect the habui-conditional and viceversa. It is hard to determine if these were "mistakes" or the expression of some shade of meaning outside of our reach. Without any contemporary description of the difference this is probably destined to stay a mystery.
2. The conditional moods of Italy
This section is mainly based on the chapter Condizionale in Rohlfs' foundational monograph .
The evolution of Italian is characterized by the lack of any central standardizing effort (as opposed, e.g., to the evolution of French, that selected the Paris dialect as a standard essentially because Paris was the physical seat of the king). Hence for large parts of history the determining factor in language choice was the literary prestige of the various regional languages. As we will see, this will produce some unexpected results.
The standard rules of phonetic evolution would turn the habebam-conditional into a conditional in -ea. This can occasionally be encountered (e.g. E no lo porea dire/di sí gran guisa, come in cor la sento in Guittone d'Arezzo, Gioia ed allegranza), but by far the most common, however, is a version in ia (porria, vorria, parlaria,...).
This form conditional has, on a phonological basis, two possible sources: Sicilian and Provençal (it should be mentioned that Rohlfs is strongly against a Sicilian origin, but Devoto  seems unconvinced by his arguments and I tend to agree with him). A conditional in ia is attested in both these languages and more importantly, they were two of the most important literary languages of the early thirteen century, right when Romance literature was starting to crystallize.
Be it for literary influence, or for some other reason the ia conditional spread throughout the peninsula, displacing the ea forms where they were present.
It had to contend, however, with two other forms trying to fill the same space: the Italian form the old habui-conditional (the eventual winner, that I'll call the ei conditional: potrei, vorrei, ...) and the so-called ra-conditional, derived from Latin pluperfect indicative (cantaveram > cantara). This was the main form in continental Southern Italy, but it is essentially disappeared even in literary Italian (surviving only in the form fora, "I/he/she/it would be"). It is still quite alive in many regional languages and in Sicilian it has come to displace the ia conditional.
To summarize, when Dante and Petrarch were starting to write there were essentially three possible choices for the conditional mood: the ía conditional (derived from Latin habebam-conditional), the ei conditional (derived from Latin habui-conditional) and the ra conditional (derived from Latin pluperfect indicative). They had a very complicated geographic distribution (notably, the ei conditional was very rare in Southern Italy, while the ra conditional never climbed above the Southernmost tips of Tuscany), but the most prestigious was the ia conditional, due to its usage in Provençal and Sicilian poetry.
3. Wild speculations
How did Italian choose among the various conditional moods? Here none of the sources I consulted suggested any reason. Only Devoto  suggests that the ei conditional might be "more forceful". Moreover, from our discussion of the Latin periphrastic constructions, we see that the habui-conditional (that initially had a counterfactual value) needed to change its meaning, although there are usages in Cassiodorus that suggest just such a semantic shift. Finally, the ia conditional was by far the most geographically widespread.
And yet, Tuscan poets preferred the form in ei.
If I am allowed to speculate a bit, I would suggest that it was the predominance of a relatively minor form, the ei conditional, in a relatively small geographic and temporal area (Northern Tuscany at the end of the thirteenth century) that got blown out of any proportion due to the incredible literary significance of the works produced in the area, chiefly Dante's Comedy. It is interesting to note that Petrarch (himself from Southern Tuscany) uses the ia conditional slightly more often than Dante.
After a period of transition, where the ia conditional was used less and less in prose works, in the early fifteenth century it was definitely used only in poetic works, where it's still alive ().
 Adams, J. N. (2013). Social variation and the Latin language. Cambridge University Press.
 Devoto, G. (1974). Il linguaggio d'italia: Storia e strutture linguistische italiene dalla preistoria ai nostri giorni (Vol. 113). Rizzoli Editore.
 Migliorini, B., & Ghinassi, G. (1961). Storia della lingua italiana. Sansoni.
 Rohlfs, G. 1966-1969. Grammatica storica della lingua italiana e dei suoi dialetti. Torino: Einaudi.