Last week's and this week's parshiot each deal with laws relating to the disease of tzaarat. A metzorah is expelled from the camp until his disease has receded, as determined by a cohen. Why was this task assigned to the cohanim? Some possible reasons:
1) The metzorah was expelled from the camp. One reason given was to give him a chance to contemplate his sin. One danger of unguided contemplation is that he might end up feeling alienated and hostile instead of repentant. Weekly visits by the cohen both provide an opportunity for spiritual guidance also reassure the metzorah that while they might be isolated, their welfare is of enough concern that someone with the status of a Cohen is obliged to personally look after them.
2) A Cohen is a person of great prestige. He may enter sections of the Beit Hamikdash closed to most people. Wherever he goes receives gifts (terumah, challah, etc.) from the common folk. Having to minister to the metzorah helps drive home the idea that with his privileges come responsibilities, even to the least among his people.
3) The talmud says that the causes of tzaarat were lashon hara (slander) and gavrah (arrogance or pride). As someone at the head of the religious hierarchy, a Cohen might have been especially at risk for these character flaws. Perhaps viewing the consequences helped the Cohen from actually committing the sin.