Charles H. Spurgeon on Psalms 137:1

By the rivers. The peculiar reason for the children of Israel being represented as sitting at the streams is the weeping. An internal reference of the weeping to the streams, must therefore have been what gave rise to the representation of the sitting. Nor is this reference difficult to be discovered. All languages know of brooks, or streams of tears, compare in Scripture, La 2:18; "Let tears run down like a river day and night"; La 3:48; also Job 28:11, where inversely the gushing of the floods is called weeping (Marg.). The children of Israel placed themselves beside the streams of Babel because they saw in them the image and symbol of their floods of tears. —E. W. Hengstenberg.