This verse reveals some of the hypocrisy of the title of the hymn. Kipling calls colonialism the white man's burden, but history shows us that colonialism in practice was less of a burden than an opportunity for the colonizer to enrich itself; colonization was more often inspired by greed and gluttony and the constant search for more.  

Kipling's poem suggests that through colonization, the "white man" can bring peace to the savage natives, end their hunger, and make them prosperous. As the white man gets closer and closer to the end goal of "peace," the natives can expect an end to their way of life.  

At the end of the verse, Kipling warns about the dangers of success if the white man is able to take on this burden. By colonizing the heathen land and civilizing the natives, the white man can expect the natives to become lazy and to continue barbaric religious traditions. The power and control that the colonists worked so hard to achieve and the effort they will spend to "civilize" the natives and make the land prosperous may "all be for naught" (or all for nothing).

Today, knowing all that we do about how imperialism usually played out, we may read this and think that it is satire. Unfortunately, no such luck; Kipling was serious.

As with the rest of this poem, the third verse is a warning to the United States about what it can expect when it takes the Philippines and tries to administer it as a colony.  In this verse, Kipling is focusing on the idea that the colonized people will destroy everything that the colonizers are working for.

Kipling starts by warning that it will take “savage wars” to bring peace to the new colony.  This was true in the Philippines as the US and Filipino independence fighters fought a brutal war. 

Kipling then goes on to say that the colonizers will do all sorts of philanthropic things.  They will help the colonized do better at producing enough food to feed themselves (fill full the mouth of Famine).  They will bring better health and hygiene to the people they colonize.  But then, when they are getting close to making everything better, the colonized people will ruin everything.  They will do this because they are lazy (sloth) and because they are uneducated, uncivilized, and perhaps stupid (heathen Folly).

As with the rest of the poem, this is an attitude that we would see today as racist.  Kipling definitely glorifies the motives of the colonizers and denigrates the colonized.