Do we know how common it was for Romans to do this? This seems like a difficult stance to consume anything.

Long before the practice of reclining at table began, if that's what you're asking. The OCD lists reclining at table as first appearing among the Greeks possibly sometime around 700, though in the study of early Greece that often just means sometime around the end of the Dark Age. The practice was somewhat common in the Near East, which is where the Greeks got it from. Reclining at table is not mentioned, for example, in Homer, and only appears rather late in Roman literature. We don't know when the Romans adopted the practice, though the Etruscans were already reclining at table in the 7th Century, as evidenced by the ubiquity of the practice in tomb paintings depicting banquets (a common Etruscan tomb theme). The Romans almost certainly got it from the Etruscans, but we don't know when or precisely how--presumably it was one of many cultural practices inherited from the Etruscans throughout their period of close contact with the city. Livy dates the lectisternium, the ritual in which images of various gods were laid out on couches with a banquet set out before them, to 399. Whether this date is accurate or not, it's clear that at the very least the practice was known at a very early period. Plautus' characters routinely recline whenever eating in company, and by Cicero's time the practice was pretty much ubiquitous.

There seem to be a lot of comments on here question whether this was purely a practice of the aristocracy or not. It probably wasn't, at least by the time it was commonly adopted, though originally it almost certainly was. Certainly it was not the mark of a socio-political elite, if freedmen like Trimalchio are depicted as reclining at table and just about everyone in Greek literature does. Wealth and luxury, however, almost certainly were attached to the practice in some way. For one thing, you need rather a lot of room for a proper triclinium. And importantly, reclining at table was done when eating among companions, not by yourself. Romans and Greeks may well have eaten reclining while eating by themselves, but pretty much all of our references to reclining at table is during feasts or banquets among company. Both the Greeks and Romans ate rather lightly during the day, often on the go, and parading out the rather bulky furniture of the triclinium is rather silly for that. In connection with this most of the furniture of the triclinium was removable, particularly the tables, which would be stored away and only replaced in the room during dinner (not sure about the couches--some of them appear to have been really heavy). It's safe to say that reclining at table would not have been necessarily common except when company was over--in every society private dinner parties tend to be the reserve of the wealthy and connected, but that's not to say that rich Romans were attending dinner banquets every night. That it was a practice connected with high culture is obvious--Aristophanes' depiction of Philocleon as an antiquated old rube is reinforced by the fact that he has to be taught how to recline at table. It was also very ritual, which would've been very important among all classes and social strata. Both at Rome and Greece public banquets were laid out with couches--at Athens we have evidence of the massive public dining rooms on the Acropolis, obviously laid out to fit huge numbers of couches (although the exact arrangement of the couches is debated), and the massive public banquets often paid for on religious occasions by private politicians at Rome are usually described as being laid out with couches. It's also interesting to note that there is evidence for reclining at table in pretty much every Roman province at some point, but I don't know much about archaeology so that's all I can say on that.