In "The Merchant of Venice", what reasons does Antonio give for his being melancholy?

In sooth, I know not why I am so sad;
It wearies me; you say it wearies you;
But how I caught it, found it, or came by it,
What stuff 'tis made of, whereof it is born,
I am to learn;
And such a want-wit sadness makes of me,
That I have much ado to know myself.

These are the first lines of the play - and the answer to your question. Antonio actually doesn't give any reasons for why he feels sad: in fact, the whole of the first part of this first scene is given over to discussing it. His friends inititally suggest that he is worried about the merchant ships he has on the ocean:

Your mind is tossing on the ocean;
There, where your argosies, with portly sail,—
Like signiors and rich burghers on the flood,
Or, as it were, the pageants of the sea,—
Do overpeer the petty traffickers,
That curt'sy to them, do them reverence,
As they fly by them with their woven wings.

When Antonio rejects this explanation, Salanio has another one standing by:

Why, then you are in love.

And Antonio's response?

Fie, fie!

And that's all that's said. What does "fie, fie" mean? I suppose it's quite like "shut up!" or "stop it, stop it" - it's not quite a "no", but it's certainly not a "yes". Many critics - and if you carry on reading Act 1, Scene 1 you'll see why - have argued that Antonio's sadness is because he is in love with Bassanio. But does Antonio ever connect the two things? Nope.