I would like your thoughts on an idea. What if Con was needed to hit with heavy weapons and sniper rifles while sniping? With heavy weapons, I would argue that you use your body steady the weapon and absorb the strain. While sniping can easily be as much about endurance as hand eye coordination. Right now I am just playing around with ideas.
No, that's a terrible idea.
Heavy weapons already require str 12 or 14 to use.
Sniper weapons are generally worse than equivalent level longarms. They have roughly the same amount of damage dice, but are unwieldy. Which means they can only be fired once per round. And you have to use a move action (IIRC) to use the extra range of it, except that the extra range isn't that useful given the normal range of combats (because engagements tend to happen at 60ft or less and because you quickly run out of table space to set up the combat grid). Sniper weapons are in general terrible. Another complication to sniper weapons is that where the sniper rifle shines (extreme range) it pretty much relegates everyone else to doing nothing, which while not a game balance problem is a significant problem for overall table fun.
So, anything that makes sniper weapons more difficult to use when they're already worse than your average longarm is a bad idea.