apply logo and suitable for different sizes

Now you can play with more than one image at once. When you remove /**/ characters from the code it will work even on subfolders. I mean it's going to copy a tree of all nested folders and make their duplication. That new tree with a main folder (old name with "logo") will be created next to original one. So the structure of (sub)folders and files they contain remain the same. Difference is that each image will be saved with logo. Anyway that multi folders option probably won't be useful for you. One level folder should be completetly sufficient.

function FSf(sF, dst, i) {
     if (sF && !dst.length && !i) {
          Folder(decodeURI(dst[0] = fld = sF.parent + '/' + (nme2 = (nme1 = decodeURI(sF.name)) + ' Logo'))).create()
     }
     for(sF = Folder(sF).getFiles(); i < sF.length; i++) {
          if (sF instanceof Folder) {
               dst.push(eval((r1 = 'decodeURI(sF') + r2 =').replace(RegExp(nme1), nme2)'))
               /*if (i) fld = dst[0]; Folder(File(fld += '/' + sF.name)).create(), FSf(sF, dst, 0)*/
          }
          if (/\.(jpg|psd)$/i.test(sF.name)) {
               displayDialogs = DialogModes.NO, preferences.rulerUnits = Units.PIXELS, open(sF)
               d = 20, m = 3, (h = (aD = activeDocument).height) > (w = aD.width) ? s = w : (s = h, d /= 2, m /= 1.5)
               aD.selection.select([[(f = h / d), f * (d - m)], [m * f, f * (d - m)], [m * f, f * (d - 1)], [f, f * (d - 1)]])
               function loop(v1, v2) {for(j = v1; j < v2; j++) v1+= hst; return v1}
               blk = loop(0, l2 = (l1 = (hst = aD.histogram).length) / 2), wht = loop(l2, l1)
               open(File('~/desktop/watemark/logo_' + (blk >= wht ? 'white' : 'black') + '.png')),
               (log = activeDocument).resizeImage(s / 7.5), (sel = log.selection).selectAll(),sel.copy()
               log.close(dnsc = SaveOptions.DONOTSAVECHANGES), aD.paste(), (jpg = new JPEGSaveOptions())
               .quality = 12, aD.saveAs(File(fld.match(eval(r1 + '.path' + r2)) + '/' + sF.name), jpg), aD.close(dnsc)
          }
     }
}
FSf(Folder.selectDialog('Please select top level folder'), [], 0)

EDIT: this is a version letting you decide where you want to put your logo (corners, sides, or in center) / just edit pos(obj.bL):

function FSf(sF, dst, i) {
     if (sF && !dst.length && !i) {
          Folder(decodeURI(dst[0] = fld = sF.parent + '/' + (nme2 = (nme1 = decodeURI(sF.name)) + ' Logo'))).create()
     }
     for(sF = Folder(sF).getFiles(); i < sF.length; i++) {
          if (sF instanceof Folder) {
               dst.push(eval((r1 = 'decodeURI(sF') + r2 =').replace(RegExp(nme1), nme2)'))
               /*if (i) fld = dst[0]; Folder(File(fld += '/' + sF.name)).create(), FSf(sF, dst, 0)*/
          }
          if (/\.(jpg|psd)$/i.test(sF.name)) {
               displayDialogs = DialogModes.NO, preferences.rulerUnits = Units.PIXELS, open(sF)
               s = (h = (aD = activeDocument).height) > (w = aD.width) ? 0 : .75
               obj = {
                    tL: [1.5 - s, 1], tC: [7, 1], tR: [12.5 + s, 1], mL: [1.5 - s, 7], mC: [7, 7],
                    mR: [12.5 + s, 7], bL: [1.5 - s, 13], bC: [7, 13], bR: [12.5 + s, 13]
               }
               function pos(v) {
                    w1 = v[0], w2 = w1 + 1, h1 = v[1], h2 = h1 + 1, aD.selection.select
                    ([[w * w1, h * h1], [w * w2, h * h1], [w * w2, h * h2], [w * w1, h * h2]])
               }
               function wh(v) {return v / 15} w = wh(w), h = wh(h), pos(obj.bL)
               function loop(v1, v2) {for(j = v1; j < v2; j++) v1+= hst; return v1}
               blk = loop(0, l2 = (l1 = (hst = aD.histogram).length) / 2), wht = loop(l2, l1)
               open(File('~/desktop/watemark/logo_' + (blk >= wht ? 'white' : 'black') + '.png')),
               (log = activeDocument).resizeImage(null, null, aD.resolution), (sel = log.selection).selectAll()
               sel.copy(), log.close(dnsc = SaveOptions.DONOTSAVECHANGES), aD.paste(), (jpg = new JPEGSaveOptions())
               .quality = 12, aD.saveAs(File(fld.match(eval(r1 + '.path' + r2)) + '/' + sF.name), jpg), aD.close(dnsc)
          }
     } 
}
FSf(Folder.selectDialog('Please select top level folder'), [], 0)