No, perspiration is not the cause of your burning eyes.
You are describing severe dry eye. Eyelid surgery will not help your dry eye but it will make it much, much worse. Blepharoplasty will weaken the blink mechanism of the upper eyelid. For many, this is inconsequential but not for individuals with dry eye. I recommend working very closely with an ophthalmologist who is actually interested in providing dry eye care (not so easy to find).
Upper eyelid surgery for hooded eyelids
From the very limited photograph, it appears that there is significant excess and loose hooded skin on the upper lids. The eyebrows appear to be in normal position. An upper blepharoplasty procedure can accomplish removal of excess skin over the eyelids. For many examples, please see the video and the link a below
Sagging eyelids may capture perspiration and track it into the eyes. It may also turn the eyelid margins inward enough to cause irritation of the eyelid glands (meibomian glands) on the ocular surface. If you have horizontal laxity as well, that my cause inflammation and papillary reaction (conjunctival inflammation) on the back of the lids. You may find that adding treatment with lubricating ointment on the eyelids at night and hot compresses in the mornings help your symptoms - be sure to avoid rubbing. Other treatments may be suggested by your Ophthalmologist or Oculoplastic surgeon. Cautious surgery of the eyelids and brows - without over-zealous removal of skin - will likely help your peripheral vision without risking worse dry eye symptoms. An Oculoplastic surgeon has experience with ocular surface problems, eyelid/ brow surgery, treatment of potential adverse effects of surgery. I would recommend seeking evaluation with an Oculoplastic surgeon because of your symptoms.
Upper lid surgery can be covered by insurance
It is possible that your eye complaints are caused by perspiration, but that would not be the first thing that I would consider. You may have dry eyes and should see an ophthalmologist for this. There are good treatments now for dry eyes other than just lubrication.
Cosmetically, however, you do have severe upper lid skin excess. You can have visual field testing performed to see if you have a peripheral vision loss. If you fail the test, you may have your upper lid surgery covered by insurance. Your physician could determine if you need a brow lift at that time, as well, but your photo is not adequate to tell.