The reasons for Manolin's tears are not entirely clear. There is evidence and subtext, however, that we can use to guide our interpretation.
On the simplest level, Manolin loves Santiago and cries because Santiago is wounded and spent on his return to land.
Manolin shows great concern for Santiago’s health, especially after he sees how Santiago has suffered in catching the big marlin.
Reading further, the relationship between the old man and the boy is one of instruction and mentorship. Also, a symbolic reading of the relationship is available.
Manolin respects and even reveres Santiago. He is, so to speak, Santiago's disciple. This is true on a symbolic and a literal level. Discipline is the hallmark of Santiago's character, his approach to fishing, and his spiritual outlook. This discipline is what Manolin seeks to learn from the older man.
Manolin is seen as a disciple who respects and loves Santiago as his teacher.
Manolin's tears, as a literal disciple of Santiago, can be seen as a measure of his knowledge (he knows how much Santiago risked and suffered at sea) and a measure of his lack of strength and discipline. He has not learned to accept suffering with dignity.
Symbolically, Santiago has often been read as a Christ figure, suffering wounds resembling stigmata and bearing his mast like a cross up the hill into town after his three days of suffering at sea.
Manolin's tears, seen in this light, are a recognition of the sacrifice Santiago has made to bring in the carcass of the great fish.