The speaker is the scales of justice, but unlike justice, he doesn't seem to be blind. We're talking about the classical image of justice as a blindfolded woman holding up a scale that symbolizes the weighing of two different points of view. (Here's a picture.) In this poem, the two sides of the scale are those who think the world will end in fire and those who think it will end it ice. The speaker believes he has acquired enough wisdom and worldly experience to "weigh in" (yes, that's where the expression comes from) on the dispute. He has experienced enough desire to know that its effects can be as destructive as they are pleasurable. But he has also known hate, either as a victim of it or, more likely, as someone who has felt hatred.
The speaker seems to be a person who has known hardship and suffering in his life. He's cautious and ironic, as we know from the ridiculously understated ending. He's not a Chicken-Little type. In fact, he doesn't seem too worried about how soon the end of the world comes, or what brings it about. At the end of the poem, he delivers his verdict – both sides of the scale seem to be weighed evenly. Or, at least, it doesn't matter whether they are weighed evenly, because after fire and ice are done with them, those scales are totally toast.