I am a skinny person, and I drink only 2 cups of coffee per day, tops, and I suffer the exact same withdrawal symptoms. Once I feel the symptoms it's too late, Advil doesn't help, coffee doesn't help, I can't look at screens for long, all I can really do is lay in bed and try to sleep it off.
However, I've learned that I have a window where I can sense symptoms might onset in the next couple of hours, and if I take an Advil then I'll avoid the symptoms.
I really need to try the nootropics everyone recommends. Coffee really only helps me power through semi-mindless work, if I need true clarity and original thinking I have to get comfortable in a quiet place and let my mind wander, and coffee doesn't help with that. (And while we're here I'll just say that's why I'm an advocate of remote setups for programmers, unless you only have semi-mindless work to do at your office).