weeping - for their past sins which caused their exile (Psa 126:5, Psa 126:6). Although they come with weeping, they shall return with joy (Jer 50:4, Jer 50:5).
supplications - (Compare Jer 31:18, Jer 31:19; Jer 3:21-25; Zec 12:10). Margin translates “favors,” as in Jos 11:20; Ezr 9:8; thus God’s favors or compassions are put in opposition to the people’s weeping; their tears shall be turned into joy. But English Version suits the parallelism best.
I will cause ... to walk by ... waters ... straight way - (Isa 35:6-8; Isa 43:19; Isa 49:10, Isa 49:11). God will give them waters to satisfy their thirst as in the wilderness journey from Egypt. So spiritually (Mat 5:6; Joh 7:37).
Ephraim - the ten tribes no longer severed from Judah, but forming one people with it.
my first-born - (Exo 4:22; Hos 11:1; Rom 9:4). So the elect Church (2Co 6:18; Jam 1:18).