I don't think added weights will help enough to notice. Sliding your weight forward sounds helpful.
I was going to suggest a pricey slick tire with grippy rubber, as wide as will fit.
These Rene Herse tires are the extreme example, very grippy, 2.3 inch wide, and $$$.
Rat Trap Pass 26x2.3
A few complications, though:
It looks like only the front wheel has brakes? is it a drum brake or a rim brake?
Rim brakes will also limit the tire width. How wide can the brake pads separate when when they are unlatched from their riding position for wheel removal?
Low pressures will help. For a reasonable pressure, I'd look for a slight widening of the tire sides where they contact the road. Since the weight on the tire seems low, this might be quite low pressure! The "rule of thumb" on a road bike is a 15% height drop where the tire flattens against the road with the rider's weight on the tires. That allows flexing over rough road surfaces, but with minimal pinch flat problems.
You are depending on this one wheel for steering and braking, so flats on a downhill would be bad. That kind of limits just how lightweight a tire you would want.
And too low a pressure makes pinch flats more likely. But pinch flats are related to how
tall and how
sharp edged the pothole / rock / debris is, and
how fast the rider is going. The tire just bumps over a squared rock chunk at low speeds, but compresses to the rim at high speeds, causing the pinch flat.
Tire width vs pressure.
Pressures are proportional to the square of the width (the interior circular cross section is that familiar formula, pi x radius squared)
A 2 inch tire has about
75% more air volume than a 1.5 tire! Surprising. So maybe 25 psi on a 2 inch tire instead of the 40 psi on the 1.5 tire.