One of the justifications of colonizing by Europeans was that they had an obligation to "better the lives" of the people they conquered. So, they were not actually doing it for (primarily) profit, but as an obligation, a duty to act for those people.
Send forth the best ye breed
Only the bravest, strongest go forth as colonizers and soldiers
Go bind your sons to exile
Just getting to some of the colonies took months; it would be
years or decades before many would or could return to England
To serve your captive's need
Again, the purported reason was to better the lives of the natives
To wait in heavy harness
The average soldier wore uniforms and carried gear that weight over
Take up the White Man's Burden
ye dare not stoop to less
Nor call to call on freedom
to cloak your weariness..
The rest of this stanza refers to the fact that the conquered will judge your fitness to rule them by every action word and deed done. A failure to act appropriately will result in uprisings and more strife. A job well done, no matter how exhausting it is, will result in successful assimilation.
The last stanza points out that the military conquest of natives was relatively easy (given technological superiority and military disciple) and the conquerors could look forward to being cheered at home, earning promotions and honors. The real work of empire building is done by those who stay in often inhospitable conditions and surroundings to do the work of empire.
While to some degree this poem may be looked on as being condescending, Kipling's focus is not on the natives, but on those responsible for making the conquered lands part of the Empire. His references to the natives as "half wild half child" are reflections of how most British viewed them. The poem is not about trying to prove to the British the natives were or were not inferior; he merely reflects the common sentiments of the time here. In other of his poetry, he makes the point that virtues like heroism, integrity, courage, and pride are not unique to Europeans, but can be found in all cultures. So don't read more into the poem than is there.