"Why were the armies of the Eastern Roman Empire in the 6th century so much smaller than the Roman armies fielded during the Roman civil wars?"

Short Answer

The Eastern Roman Empire had small field armies during the 6th century because it was almost bankrupt and therefore couldn't afford to raise large armies.

Long Answer

I'd like to start by clearing up a common misconception - the overall size of the later Roman army was actually bigger than it was during the times of Augustus and Trajan. Under the reign of Tiberius the army was about 255,000 men - 125,000 legionnaires, 5000 praetorians, and 125,000 auxiliaries. The Roman army of the early 5th century was theoretically about 400,000 men in total, but was understaffed so was probably closer to 300-350,000. The early imperial army was organised into legions, large bodies of thousands of men that regularly fought, whereas the later army was organised into comitatenses; fighting units of 1000 men each. Furthermore, most of the later Roman army were the limitanei, which were border garrisons who were rarely involved in campaigns. This means that even though the later Roman army was very large, most of its units did not go on campaign, giving the impression that the later Roman army was far smaller than it actually was. Obviously, when the western half of the empire fell the western armies fell with it. Despite this loss, the ERE could still maintain an army of around 200,000 men. I mention this because the Eastern Roman armies of the 6th century were not typical and should not be seen as representative of the Eastern Roman Empire as a whole.

The reason the size of Roman armies took a nosedive in the middle of the 6th century is as a result of emperor Justinian and his incredible spending habits. Justinian haemorrhaged money. His vast building programmes, expensive treaties with the Persians, and most of all his attempted reconquest of the west bankrupted the empire. The reason Belisarius had only 7,500 men to start taking Italy (he did get reinforcements later in the campaign) was because that was literally all the emperor could afford to spare at that time, and he removed the limitanei from the Danube river to create this army. When he invaded North Africa just before this campaign, Belisarius had around 17,000 men, but had to leave half of them behind as a garrison. Procopius' The Wars tells us that Belisarius was almost constantly asking Justinian for more money, supplies and men. Even then, a lot of the men went unpaid and the garrisons of North Africa mutinied in 536 because they had not been paid for years. From this we can suppose that the imperial treasury was empty - not in a figurative way, at times it was literally empty and the army couldn't be paid. There was also the first recorded outbreak of Bubonic Plague in 541, which killed about 25% of the empire and further limited sources of tax income and soldiers. According to the chronicler John Malalas, in 553 Justinian attempted a drastic debasing of coinage so he could mint more coins and pay the army, but rioting across the empire followed and the policy was scrapped. In the late 540s and early 550s in particular, the sources paint an almost uniform picture of an empire on the brink of financial collapse because of wars and plague. Justinian probably did have some money left, but the empire was certainly losing money fast.

This was not helped by the wars in Italy. You say that Belisarius retook Italy with 7,500 men, but in truth he did not have control. In 540 AD, Belisarius entered Revenna, the Gothic capital, and declared mission accomplished. There was then a 13 year war between Belisarius' men and a Gothic insurgency led by Totila. The war devastated the region - when Belisarius retook Rome for the second time (Totila conquered it in 549) he found nobody there; even Rome itself was abandoned by its inhabitants as a result of the war. Even once the Goths were fully defeated in 554, the Exarch of Revenna and the Bishop of Rome routinely wrote to Constantinople asking for money to rebuild - Italy was a money sink. North Africa did not go much better - in the 540s the Moors unified to fight the Romans and the Romans could not pin them down, which meant another protracted war, though North Africa did eventually become profitable. In the 550s and 60s, Avars and Bulgars got in on the carnage and raided the Balkans as far as Constantinople's suburbs. There were supposed to be garrisons along the Danube to prevent this, but the troops had been stripped from them to fight for Belisarius and the empire could not afford replacements. The Long Walls, Constantinople's first line of defence, was completely unmanned and the Avars were able to reach the suburbs of Constantinople before facing any notable resistance from the army at all. The whole episode was farcical and costly, and a focal point of Procopius’ anger toward Justinian. From the 530s well into the 560s, the empire was broke and therefore unable to raise armies.

The extended territory created by Justinian's reconquest stretched the Roman army even thinner and even more units became limitanei. Southern Spain, North Africa, and Italy all needed extensive garrisons which took men away from the mobile field armies. By the early 7th century, the situation had recovered and field armies were once again in the tens of thousands, but never the 70,000 men that was previously typical of major wars (see Vitellius' army during the Year of Four Emperors, or the Roman army that fought the Jewish War). That being said, even during the Last Great War of Antiquity (608-28), a climactic war of attrition between the Eastern Roman Empire and the Persian Empire, Roman armies were always over 20,000 soldiers despite suffering serious losses of territory and men throughout the war.

Sources:

Mitchell, Stephen. A history of the later Roman Empire, AD 284-641. John Wiley & Sons, 2014

Cameron, Averil. Procopius and the Sixth Century. London: Duckworth, 1985.

Scott, Roger D. "Malalas, the secret history, and Justinian's propaganda." Dumbarton Oaks Papers 39 (1985): 99-109.

Sarris, Peter. Economy and Society in the Age of Justinian. Cambridge University Press, 2006.

Evans, J. A. S. The Age of Justinian the Circumstances of Imperial Power. London ; New York: Routledge, 1996.

Moorhead, John. Justinian. Routledge, 2013.

I answered a similar question about the size of Belisarius' army in Italy https://www.reddit.com/r/AskHistorians/comments/96nmcf/when_belisarius_was_sent_to_reconquer_italy_he/e42qc68/ and explain some of the reasons that Justinian may have had for sending Belisarius to Italy with only 7,500 men (and also why those 7,500 men weren't as "small" of a force as we perceive them to be). That being said, Eastern Roman armies actually weren't smaller in the 6th century. When Belisarius retook North Africa from the Vandals he actually had around 15-17,000 men with him. On top of this the total strength of the Eastern military at this time was around 200,000 men. As my linked answer explains, Justinian initial sent Belisarius to capture Sicily, and sent a separate army commanded by Mundus to capture Dalmatia, both of which would have allowed the emperor to reinforce Belisarius should the need to do so arise. The size, and composition, of Belisarius' army was most likely a strategic choice that served several purposes. One of these purposes would have been to trick the Goths into thinking that it was just a garrison force heading for Carthage, and that they were simply stopping in Sicily for a short time. Another purpose would have been the added mobility that came with an army of this size that was composed of large number of cavalry. It should also be noted that while the Eastern military totaled about 200,000 men, that these men would not have all been available for the Gothic war. Some of them would have been needed to defend the Danubian border, which was fairly long, and some of course would have been needed along the border with Persia (with whom the Romans had been at war with only 4 years before Belisarius went to Italy). In fact the Persians broke a peace treaty with the Empire in 540, while Belisarius was still fighting in Italy.

Sources: Warfare in Medieval Europe, Bernard S. Bachrach and Davis S. Bachrach

If you read the first few paragraphs of chapter 5 of the Gothic Wars 1, which is handily free and online as copyright has expired on H.B. Dewing's translation (see here: https://www.gutenberg.org/files/20298/20298-h/20298-h.htm#Page_1 ), then you will see that there were three invasions of Italy, not just Belisarius'.

Mundus: "And he first commanded Mundus, the general of Illyricum, to go to Dalmatia, which was subject to the Goths, and make trial of Salones."

The Franks: "And he also sent a letter to the leaders of the Franks as follows: "The Goths, having seized by violence Italy, which was ours, have not only refused absolutely to give it back, but have committed further acts of injustice against us which are unendurable and pass beyond all bounds. For this reason we have been compelled to take the field against them, and it is proper that you should join with us in waging this war, which is rendered yours as well as ours not only by the orthodox faith, which rejects the opinion of the Arians, but also by the enmity we both feel toward the Goths." Such was the emperor's letter; and making a gift of money to them, he agreed to give more as soon as they should take an active part. And they with all zeal promised to fight in alliance with him."

Finally, Belisarius: "As for Belisarius, he put in at Sicily and took Catana."

Belisarius was essentially invading a country denuded of soldiers, as the Goths were focussing on the North to fight Mundus and the Franks.

It's worthwhile taking Belisarius out of the spotlight of history at times to really appreciate why he was successful.

Sources: Procopius, Gothic Wars 1/History of the Wars V, Chapter five, lines 44-50.