The Song military strength was not necessarily weak, but mismanaged. Consider that they have the largest population of any nation, sedentary or nomadic, perhaps many times over. Consider also that the scientific advancement in the time of Song China enabled them to utilize the world's first gunpowder weapons, their agricultural production surpassed that of the European contemporary continent giving them plentiful supply, the Song economy produced so much each year that the 300,000 units of value paid to the Jin as tribute was intended to be 3 million but that the Jin were happy with the former, and the Song navy boasted the greatest ships in the East or West for another 300 years.
They weren't weak, but what they did have is a poor military system. Song soldiers could serve until long after they were able bodied enough to perform in that capacity and often did because they had no recourse to leave. The Song military institution as a whole was looked down upon by the scholar-official literati, and many of them were often put in military posts they were ill-suited to hold. The Song imperial army was focused primarily around the capital in order to prevent a challenge of imperial power in the provinces, and as such curtailed their ability to respond to border incursions. The "War Party" as it was called was constantly sabotaged and undermined by the officials at court and the ineptitude of the Emperors, as seen most prominently with the tragedy of Yue Fei.
It's easy to find fault with the Song as Chinese historiographers have done for a long while, due to their failures against the Khitans, Jurchens, and Mongols. However this failure falls primarily to the inability of its leaders, more than the inability of its soldiers, which is a result of the strong cultural focus of the Neo-Confucian scholar-elite era. At the command of a gifted strategist and logistical wizard, and with the backing of their country, the Song no doubt could have amounted to a reputable military force.