If you take the screenshot you posted and play around with the color balance (reduce green/blue), you'll see that there's still a red border around the "thinner" font, it's just lighter because of the alpha blending. With the black background it's more prominent, but it's still there with the white background. You could play around with the blend modes or the alpha cutoff of the font to tweak it to your liking. Right now you have a very large soft border (a couple pixels it looks like), but if you make it a sharper cutoff (or discard when alpha < .25 or something, but still keep the alpha blending) then the font will start to look the same regardless of the background, while still keeping a soft (just thinner) border around the glyphs. It will still vary a bit depending on what you're blending the font over, but it will be less prominent than what you currently have. Playing around with the blend modes can change how it looks too, but blending is always part of one, the rest of another, so it will always vary based on what you are blending over.