Training advice for lifting with light weights only?

[Zephyr10]

So I have a lil problem. If anyone can help me that'd be appreciated.
I've been an exceptionally skinny guy my whole life, i'm 19 now. Recently taken somewhat of an obsession with gaining weight and bulking up, don't think I'll have too much trouble with eating for that but the problem is the workouts.

See, since early childhood I've had pulmonary hypertension (PH for short, google if you're curious but it's basically a heart condition that causes high blood pressure in the lungs) and that's always put quite the limit on any physical activity I can do. I wanna get into a proper workout routine, the thing is I'm not sure if there's a point. Doctors have told me working out is fine - encouraged even, but I've been warned to not lift above 20lbs (total, that means only 10 for each arm). Which is extraordinarily light and has got me discouraged, thinkin I could never possibly make any sort of progress with such light weights, and no progressive overload.

Basically what I'm asking is, is it possible to get fit only lifting such light weights? I always thought just increase the reps I do to absurd heights since that's all I'm really able to change, but I really don't know if there's a point. I've been having a really hard time trying to figure out a nice routine that works for me