I've never heard of eyelid weights being used after a facelift.
Your situation must be more complicated than the description. Eyelid weights are used for neurologic problems where the eyelid does not have the mechanical ability to close. This should never be a product of the facelift.
Eyelid weights after face lift
I assume that you had a face lift and upper lid blepharoplasty and now have and eyelid that will not close.
There are a number of reasons for this problem - the amount of skin removed, nerve damage, or (if ptosis was corrected at the same time), an imbalance of the nerve supply to the levator muscle that opens the upper lid.
Permanent implantation of weights at 2 weeks seems early, except for a documented nerve injury.
There are other, temporary ways to protect the eye - if there is a possibility of nerve recovery.
Before anything is done consult a Board Certified Opthalmologist specializing in nerve injuries of the eye to discuss what has happened and be sure the treatment and the timing makes sense for you. Best wishes.
I'm not entirely clear on your situation as to whether you had a facelift and injury to the facial nerve resulting in incomplete closure of your eye (lagophthalmos) or if this was a preexisting injury. I would not have expected a facelift to help with that. In either case, that doesn't sound like a good situation, so I wish you well. In response to your questions about gold versus platinum implants, I prefer platinum. Both gold and platinum are inert (do not react in the body). As you know, both are heavy precious metals. Platinum is about 10% more dense than 24K gold and therefore can be about 10% smaller and have the same mass. The weight will distort the normal contour of the upper eyelid and because of that, you want one that is small and has a low profile. If you are concerned about the appearance (most people are), then the more important thing to know is that there are normal contour implants and "thin profile" implants. The thinner the profile, the less bulky it will appear in the upper lid. I prefer to use platinum "thin profile" implants, but obviously speak to you surgeon about this. I hope this helps and best of luck with this difficult situation.
Eyelid implants after nerve injury
In reading your post, I'm realizing that you recently had a facelift and also have nerve injury which is requiring eye protection due to a paralytic exposure of your cornea. The choice to undergo eyelid implants is one made by functional eye examination and tear production tests. Both gold and platinum implants work well, it really comes down to expertise in managing facial nerve paralysis. There is also functional testing that should be done in order to rehabilitate the face.