I think 'faintly' in this case stands for 'lightly', 'with lightness', or something like that, meaning that the bridge, despite its bulk, was designed with a lithe, a lissome outline. However, a native speaker should explain it better than me.

It is somewhat poetic or creative writing. Clearly, the idea is that something about the bridge is so thin and so light that the bridge is almost hard to see, as if it were drawn faintly, using a hard pencil and pressing lightly. This sounds like a description of the bridge designs of Othmar Ammann, designer of the George Washington Bridge and other great New York bridges, who used new materials and technology to built very thin, light bridges, in comparison to the solid, monumental look of the Brooklyn Bridge. Let's see if I'm right. Yes, I just Googled and I find this is from a description of the Verrazano-Narrows bridge, also designed by Ammann. In the original, I see that the phrase "an enormous object drawn as faintly as possible" are placed in quotation marks and are the actual words of Ammann. Actually, they were a bit too light, as it was discovered, after the Tacoma Narrows bridge collapse that many bridges were too subject to buildup of oscillation in wind, and a number of Ammann's bridges needed to have stiffening structures attached, making them less light.

The word faintly in this context would mean that the enormous object was drawn as lightly as possible. That would mean it would have been difficult to see the lines of the drawing.

Perhaps I should say that "faint" means "hard to see, not bright, not clearly defined." For example, in the night sky the Milky Way is faint. Reflections in a mirror are bright, but reflections in glass window are faint. On a foggy day, things in the distance look faint.