Song China taxed the merchant class to pay for the military, as did every state until the 20th century. The UK, too, had high military spending by today's standards, and the taxpayers viewed the tax burden of the 19th century as barely tolerable; total government spending in fact was about 10% of GDP.
When I proclaim the Song militarily weak, this comes from e.g. the dynasty's indifference to maintaining control of barely populated areas like Tibet and Xinjiang. This is why it was constantly threatened, of course.
I'm less sure about the part about limited government. I'm basing this on Dieter Kuhn's The Age of Confucian Rule and Timothy Brook's The Troubled Empire. Brook claims that the Yuan dynasty introduced absolutism into China, building upon past Song developments, contrary to Western claims that China had always been absolutist. Kuhn contrasts the aristocratic Tang with the mercantile and Renaissance-like Song; from his description, neither era comes off as absolutist, which is probably why China was so prosperous in both the Tang and the Song eras, whereas under the Ming and especially the Qing it was stagnant while Europe surged ahead.
I wouldn't say that spending 5/9 ~ 5/12* of total budget on military maintenance a "relatively low" spending
at peace. And the bureaucracy was only small at the beginning, according to Sima Guang, the number of bureaucrats around 1050(90 years after the founding of Song) is ten times larger than when Song was founded.
While the spending was huge, it is true that the actual military was weak, it's a long story but I'll make it short:
Song was founded in a troubled time with barbarian at doorstep and its northeastern border was a plain―a previous warlord sold the easily defensible parts to the Khitans to show good will. So Song had a policy that encouraged people to join the army. Initially there wasn't much problem as soldier wasn't exactly an easy job, and throughout Taizu's reign(960~976) the number of military personnel was around 400 thousand men.
Later, Song underwent a rough Enclosure analog and many former serf/peasants became free but unemployed, however, unlike England, there wasn't a big requirement of labors in Song China, so these job seekers end up in local recruitment stations and the result was the 1.25 million men army during Renzong's Qingli era(1041~1048)
This gigantic army, however, wasn't as affordable as it was when only a quarter as large, so the quality deteriorated severly, and contemporary sources stated that some soldiers were seen peddling goods and paintings in markets while others hired people to carry their own rations, and most men hadn't seen a war in their life**.
* 50 mil
guan out of either 90 mil
guan(1048) or 120 mil
guan(1049).
** Song had not fought any wars with the Khitan Liao after the Chanyuan Treaty in 1005, and the war against Xi Xia in 1040~1042 was regional and a military disaster for Song as they lose all three major battles, though it was also an economic disaster for Xi Xia so it ended in status quo.
By the way, Song dynasty used to have fixed exchange rate between coin, grain, silk and silver for tribute, trade and accounting purpose, but was effectively abolished by Wang's reform in favor of a pure monetary system. So it is beneficial for a more liberal market.
And actually the Conservatives were only at the helm between 1085~1093, Wang's reformations were reapplied in 1094 and Reformers dominated politics all the way to the end of Northern Song in 1126. However the two factions were constantly feuding all along and crippled the government.
I don't 100% agree with Kuhn, while court politics were more absolute during Ming and Qing, it wasn't really better during Tang and Song, where Yue Fei can be executed for no reason at all(maybe Jurchen Jin's secret demand)
And Ming and Qing weren't stagnant at all beside Qing's reluctance to accept firearms, as they will give Han people an easy way to defeat steppe people like themselves.