It's a standard side effect of the combination of:
- Not quite enough gas/rpm on the engine and
- Lifting the clutch to biting point a little bit too quickly and
- A little bit of play in the rest of the drivetrain components
Essentially it's a bit like bouncing a ball, and then the tiny bit of continuous effort required to keep the ball bouncing.. Or it's a bit like shutting off a tap but not all the way, and then hearing the water pipes carry on making a hammering noise. Like any resonating system that doesn't really feature anything that will dampen a vibration, hitting the right frequency at the start and maintaining a little bit of motion input will keep things bouncing..
If you're finding you can do this every time, try raising the engine speed a little, and bring the clutch up not quite as far, then don't begin bringing the clutch out (further out than biting) until the vehicle has picked up a little more speed. You're looking to make an alteration to the resonant properties of the system - a different engine speed is a different base frequency to begin with, and changing clutch behaviour is "creating less of a bang" when "bouncing the ball"/"shutting off the tap"/starting off the resonance
My partner can do this reliably in our 190,000 mile audi; nearly every set-off she makes has some drivetrain judder, whereas it seldom happens to me. We have somewhat different clutch usage habits; I tend to blip the engine speed and then catch the clutch on it's biting point as the engine is revving down, using the throttle to "catch" or lift the engine speed slightly at the set-off speed when the clutch has started biting. She lifts the clutch further/more into biting, with the engine idling or just above tickover..
Ensure your heel is on the floor and your micro clutch adjustments come from flexing your ankle rather than bending your knee, as the precision is much better from your ankle
There is, additionally, the possibility others have mooted re worn or warped clutch components meaning there's an unevenness to the friction power transfer offered by the plates, but trying a few different driving habits is cheaper than launching into a mechanical investigation. You're right that the friction components are more grabby after damp weather; this is sometimes due to surface corrosion of the friction components - a light dusting of rust that increases friction and makes it more snatchy