For M14 types, with available mounting and my body, I prefer longer eye relief options, like 3.5"+, though I am not you so...
If I'm shooting up close and on the fly, I really like 1(ish) x capability, though to a degree people can adjust to a lot. Some were running fixed 4x magnification, so I hear, universally for everything.
I would personally lean towards an LPVO for what you're describing, starting at 1x and going up as high as your farthest distance requires, but also keeping in mind that the wider zoom range, all else being equal, the more it costs, and the more it compromises something else, whatever that may be.
The other thing to consider on weight, on an M14 rifle, is that once you put on optics, between the mount, the rings, and the scope, no matter what, you're not going to make it a light and fast-swinging easy 3 gun kind of thing. People with the skill might be able to handle it quickly, but that's not the same thing.
Depending on your use, it might be also an option to use QD rings, and alternate between a red dot, or LPVO, and a higher power option.
Maybe, for instance, a Vortex PST 1-4x24 (you can get them on clearance now, and it is almost half a pound lighter than the PST Gen2 1-6x24),
Vortex PST 1-4x24
or even better deal, with MRAD...
Vortex PST 1-4x24 (MRAD)
It's kind of tempting to buy one just to get an MRAD version, though the particular MOA version I've got is just sitting in a box, so... if you can find anyone closing out the capped turrets versions, that's probably my favorite version in that model, as I'm not a turret turner, and I'm paranoid about accidentally changing turret settings, but again, you're not me...
and a SWFA 10x42 (man, you missed a heck of a sale, but still a good value at full retail).
They're both among my favorites for what they are, at least of which I've tried.