You can address several areas, other than physical fitness!
First, is your rifle on good, solid heavy bags and/or rests? In aligning the the sighting system on the target, the bags and rests should do the work of holding the sights on target, not you exerting effort. Perhaps you can move your rest system around so that it supports the rifle more solidly.
Second, does your position itself create the pulse beat? if your joints are bent, (your knees, your elbows), pretty severely, this can increase your blood pressure because your heart has to work harder to force the blood through the constrictions. Are you bent over at the waist pretty severely? Again, a really bent over position, especially if your "beer gauge" is a little large, can constrict the major arteries in you waist/hip area, raising blood pressure, increasing the pulse beat. Posisiton rifle shooters, (HighPower, Smallbore, ISU), really sometimes have to work on their kneeling or sitting position to limit pulse beat. When I shoot sitting, I unbutton the top button and let the zipper down a bit so that my pants don't cut into my "beer gauge".
Does whatever you are sitting on compress the backs of your legs? Same rationale as above. A wider bench, or a different position on the bench or chair can make a difference. When you are sitting, do your pants and belt cut into your gut? This can make a difference.
As far as position is concerned, the more relaxed and upright you are can decrease your blood pressure, lowering the pulse beat.
Quite a large number of benchrest shooters shoot a position that is referred to as "free recoil". Basically, they have stable and solid enough rests and bags that they can align the rifle sights on the target, let the bags hold it there, and really only touch the rifle with their trigger finger and maybe their thumb. They don't have the buttstock touching their shoulder, rather it is off of their shoulder by a slight amount, and the rifle free recoils back into their shoulder after a short amount of travel. They might try to keep their cheek off of the stock, or really limit how much cheek pressure they exert on the stock.