First of all, let's take a look at the wider context around this line:
Beshrew your eyes,
They have o'erlook'd me and divided me;
One half of me is yours, the other half yours,
Mine own, I would say; but if mine, then yours,
And so all yours. O, these naughty times
Put bars between the owners and their rights!
And so, though yours, not yours.
-- The Merchant of Venice, Act 3, Scene 2, Lines 14-20
She's already talking about being divided before she starts on the "one half yours" thing. I'm not completely sure what she means by being overlooked and divided, but presumably it's a reference to the way her father's will allows her only to marry a man who chooses the right casket. Thus, if she fell in love with anyone who didn't choose correctly, she would be divided between love and duty.
Thus, the concept of her being divided is already on the table, hence this particular roundabout way of "saying without saying" that she has feelings for him.
But why does she say it in such a roundabout way at all? Because she doesn't want to admit that she loves him. At this point, he hasn't "won" her yet by passing the Trial by Casket, so in some sense she isn't "allowed" to love him. Earlier on she says (lines 4-6, emphasis mine):
There's something tells me, but it is not love,
I would not lose you; and you know yourself,
Hate counsels not in such a quality.
She's denying, perhaps even to herself, that she loves him. She dares not admit it at this stage, for fear of having her heart broken if he chooses wrongly. Thus the convoluted and obfuscated language.
(Also, as someone mentioned in comments, it wouldn't be Shakespeare without some nice flowery verbiage!)