If Love Were Really Blind

[Leah S.]

Like paper lanterns in the sky
Shining against the dark of night,Get rid of the initial capitals.......?
So glow your eyes in the pale moonlight--- "So glow" bothers me, it feels awkward.
Wide and wise and tinged with melancholy.
Your lashes hang low like branches heavy with sweet peaches In visualizing this, I got the image of false eyelashes with globs on the ends weighing them down. Distracting.....
And I reach my fingers out to tug them Carrying the image forward, the narrator is now grooming the other's eyelashes.
As I swim in the pools of those green irises.
I try to walk away, to disengage from your gaze,
But I know they will haunt me, ever watching--- 'Gaze' is singular, 'eyes' would be plural. Easy fix: change 'they' to 'it'.
Fixed on and pricking the back of my neck, Funny, I also wrote a poem in which a gaze pricked the back of my neck....good image! I think you could lose 'fixed on'.
But I let them simmer. Change 'them' to 'it' since your are still referring to that simmering gaze.
Their weight burns on my shoulders until I cannot bear it anymore The whole stanze needs to change the plural to the singular. You'll be okay because you identify clearly your 'own tear-soaked eyes."
Then finally, I tremble as I turn to meet them with my own
Tear-soaked eyes.
Because I know they know If 'they' still refers to the other's eyes, then replace 'they' with 'your eyes'.
Without seeing, but rather by groping for the parts of my soul
I keep buried deep in that battle-worn chest that beats
Somewhere just south of my chest. 
Because I'm scared of surrender,
And the white flag I would once have waved
Is yellowed and tattered with age and experience. Leave off 'with age and experience.' The image implies much more, and you restrict it by belaboring the point.
Because I'm not sure how to--- dashes usually indicate parenthetical statements. If you want to emphasize a pause I'd go with .......... dots.
Let go. 
But most of all
Because I know your eyes
        will peer into mine 'peer' implies inquisitive nearsightedness. Not very romantic.
              and turn my stony heart into mush 'mush' just doesn't fit here. It made me snort, and broke the mood.
                  and render me helplessly in love. Cliché!! "helplessly in love" should be restricted to valentine's day candies. If you are going to use "render" bear in mind that the original meaning was to get the fat out of something like whale blubber by heating it up until it melted and the valuable oil was procured. So the image would be that of your lover's eyes heating up your heart until the hot liquid of love runs out? I definitely wouldn't phrase it that way, but it's an arresting image.

This whole poem is a single image of you (the narrator) attempting to turn away and resist your lover's gaze, and happily failing. Really good poems often employ a single coherent image throughout, as yours does. Carry on. Best, Leah