Apart from the regular plot, that in order to save his son he must overcome battles and so forth, what other purpose does his son have?
This is based on the fact that his son's name is Dia.
And in Krio, Dia means expensive.
Dia -> expensive
Diamond -> expensive
Is there a hidden meaning that is trying to emerge here? Or is this just a simple coincidence?
Well found question!
In short, and just from thoughts that rose at reading your translation, I suppose that name is saying that children - the movie shows enough children's abuse and misemployment - are just as or even more expensive then diamonds. 'Expensive' of course in the sense of precious.
I would speculate that it Dia's primary purpose is to develop Solomon's character further and to highlight the differences between Solomon and Archer. Solomon is a foil of Archer, and his son Dia helps to highlight that point.
While Archer is primarily driven by money and profit, having been a mercenary and now a smuggler; Solomon is motivated by his family which is setup by the initial scenes when they are talking about school.
This could even be taken a step further to say that the story of Solomon trying to find and rescue his family is a foil to the main plot of the film which is all about the diamond trade in Africa and how it is tearing the country apart.
