You have levator dehisence ptosis. Both eyes have ptosis or droopiness. The left side looks to be worse but you make a greater effort lifting the eyebrow on the right side. You also have slight redundancy of upper eyelid skin. I think it is very unlikely that you have extra fat like you think. I think it is important for you to understand that since this is reconstructive eyelid surgery, it is unrealistic to expect the two side to look perfectly like each other. I think the chance of having that type of result is very remote. This is highly specialized eyelid surgery. You need to find an eyelid surgery expert training in oculoplastic surgery. The American Society for Ophthalmic Plastic and Reconstructive Surgery has a geographic website directory that can help you find a well qualified surgeon for this type of work (asoprs.org). Please do not expect a general or facial plastic surgeon to make this repair.
Web reference: http://www.lidlift.com