Would lateral cheek fillers help lift some of the heaviness away from my lower cheeks?(Photos)

In our opinion, injectable fillers in the mid-face do not lift skin. Cheek fillers tend to make the cheeks appear wider. Based on your photos, it is possible that the fullness of your lower jaw could be from your masseter muscles. Do you have TMJ disorder, or do you chew gum? If the fullness is coming from your Masseter muscles, a Botox treatment may be excellent for jawline slimming. I hope this helps! Sincerely, Dr Joseph

Yes, you can put fillers in upper/lateral cheeks and change the proportions of your face making the cheeks your widest part of face and using the volume in your lower cheek to move some volume up. I would start high and the evaluate further.
You might decide to later try botox/xeomin/dysport etc in masseters to slim that area but might not need to once you augment upper face. I agree that you should not have buccal fat removal as I don't think that that will give you what you are looking for and is a permanent surgical procedure that you might later regret.