I think that the Borg would be just as likely to assimilate obese individuals as non-obese. I mean, it's the borg. They can always mutilate the body until it 'fits' with the look they're trying to acheive at the moment. I almost hate to let my mind wander into this direction, but they could use their saw-arms to open up the skin, and then use some sort of tube attachment to vaccum out unneeded fat tissue. If there's an exccess of skin they could wrap it around the skeletal structure, possibly producing the weird skin the Borg have, or simply remove the unneeded skin.
Heck, The Borg Queen surives with just a head, neck, shoulders, and a spinal cord sort of thing. Maybe they could take the head, neck, shoulders, spine, and organs of the obese person and plug it into a factory-line drone body.