Best glide speed varies with weight/mass. Best glide angle (L/D max) does not vary with weight but the speed to obtain that best L/D does vary.
The greater the mass, the higher the speed to obtain best L/D.
So, in still air, the same glide angle will be obtained at any mass, provided that the speed is adjusted to obtain best L/D
however; in tailwind conditions you would want to fly as slowly as possible, to take maximum advantage of the tailwind (i.e. you want to stay in the tailwind for as long as possible) therefore you should jettison mass in order to obtain best L/D at a slower speed.
On the other hand, with a headwind you want to fly as fast as possible in order to stay in the headwind for a short time, so keep the mass and get your best L/D at a higher speed.
It’s why gliders carry water ballast.