Moping melancholy mad: (13)
The first speaker calls out his buddy Terence for being such a drag all the time. This line is a great parody both of poetic language (it pokes fun at silly alliteration) and of pessimism. In his kind of crude, jokey way, he's pointing out to his friend that things aren't really all that bad, and if you pile one sad mood on top of another, you end up distorting the world, and making it seem worse than it is.
Then I saw the morning sky: Heigho, the tale was all a lie; (37-38)
This is a beautiful image of the loss of illusion. In the clear light of day, all of Terence's false and temporary happiness falls away. He's forced to confront the basic sadness and ugliness of the world without the help of the booze he'd been using to protect himself. We don't think you have to fall asleep drunk in the mud to understand this feeling. We think we've probably all had moments where the beauty of something evaporated, and left us sad and lonely.
Therefore, since the world has still Much good, but much less good than ill, (43-44)
Terence isn't a total downer. He admits that there's plenty of good in the world. On balance, though, he thinks there's a lot more bad than good. If we're looking for reasons to feel sad, we're going to find plenty of them. Because of that, he thinks it makes sense to prepare yourself for the hard times. Maybe, when it comes to sadness in the world, Terence would think of himself as more of a realist than a pessimist.