Would putting on weight help with sagging face? (photo)

I don't recommend putting on weight to try to improve this. With a facelift, the neck skin would be elevated, tightened and the excess skin removed. The jowls (which are hanging down on either side of the jaw line near the mouth) would be eradicated and symmetry would be improved. The sagging cheeks would be lifted. There is no doubt you would look significantly younger, and more fresh with long lasting results.
Sincerely, 
Philip J. Miller, MD, FACS
Double Board Certified Facial Plastic Surgeon

You don't state your current weight so it is hard to tell if you are at your ideal weight.  Fainting weight will not reverse sagging skin on your face and it is doubtful it will improve your overall appearance.  You need to make sure you are in good health, then maybe consider a facelift.  From your photo you appear to be a good candidate.

I would recommend consulting with your local board
certified facial plastic surgeon. They
will be able to tailor a customized treatment plan to best address your specific
concerns. There are a multitude of new
innovations in both non-surgical and surgical facial rejuvenation.

Based solely on your images, you may be a candidate for
structural support (Ultherapy vs Facelift), re-voluminzation procedures (dermal
filler vs fat grafting), and laser/chemical resurfacing procedures.

Gaining weight may not be the best option for improving
how you look and feel. I would not recommend using weight gain to
fill facial volume deficits.

I do not think putting on weight would be the best idea.  Find a plastic surgeon with ELITE credentials who performs
hundreds of
facelifts, necklifts, facelift revisions, and facial procedures each
year. Then look at the plastic surgeon's website before and after photo
galleries to get a sense of who can deliver the results. Kenneth
Hughes, MDLos Angeles, CA

Improving facial aging with weight gaining vs. fat transfer
to the face.Weight loss and its associated impact in facial soft tissue
volume can accelerate the signs of facial aging. It is logical to believe that
by gaining weight, the weigh loss-related facial aging could be reversed. This
is very difficult since weight gain is associated with increase of fat storage
in the areas more prone to accumulate fat (area around the belly button, love
handles, legs, hips, arms, etc.) rather than the face. Autologous fat transfer
to the face (a.k.a. stem cell facelift, see link bellow) can restore the
youthful appearance of the face in patients with mild excess of facial skin.
The procedure can also improve the expression lines around the eyes and the
mouth. The procedure can be performed under local anesthesia with minimal
discomfort (this means that the patient doesn’t need to go to sleep and
therefore it is safer). Autologous fat transfer to the face is a powerful
technique of facial rejuvenation in patients with weight loss related facial
aging.