Antonio and Bassanio share a very close bond. This is obvious when one takes into consideration to what lengths Antonio is prepared to go to help his friend, as illustrated in the following extract from Act 1, Scene 1:
You know me well, and herein spend but time
To wind about my love with circumstance;
And out of doubt you do me now more wrong
In making question of my uttermost
Than if you had made waste of all I have:
Then do but say to me what I should do
That in your knowledge may by me be done,
And I am prest unto it: therefore, speak.
Bassanio has asked Antonio for a loan so that he may woo the beautiful heiress, Portia, of Belmont. He needs the money to stand an equal chance against Portia's many other suitors, men of status and money. Even though Antonio has helped him many times before and Bassanio has, on numerous occasions, not paid him back, the merchant is still prepared to assist him - a true show of love and loyalty indeed!
Antonio is even prepared to put himself at risk by signing a bond with the Jewish moneylender, Shylock, in which the principal condition states that if Antonio does not repay the loan within three months, he must forfeit a pound of his flesh to him.
The above examples emphasize how close Antonio is to Bassanio. The implication is that their relationship is more than just friendly - they share a fraternal acquaintance with one another. One could even say that Antonio's sentiments for Bassanio go beyond that. He shows a fatherly care and affection for him. Bassanio, it seems, sees Antonio as a confidante and adviser and Antonio is more than happy to fulfill this role.
Should Bassanio successfully woo Portia, their constant companionship will somehow be disturbed because Bassanio would have to, as a matter of course, give his bride all his attention. Antonio would then, obviously, be incomplete since he would not have his closest confidante around him as much as he would want to. Many commentators suggest that it is this knowledge which makes Antonio feel sad at the beginning of the play. He realizes that he is about to lose his 'other half,' as it were, and the thought depresses him.