Sounds like you mainly want a windproof.
Something like the Rab cirrus or Montane featherlight? Typically 100gm and packs to a size of an apple. Climb in your long-sleeve thermal (or light fleece if it's chilly) then put it on at the belay. Everyone climbing on sea-cliffs should have something like this.
If you want a bit more warmth, next step up is a pertex/microfleece combo. I've got a Montbel one, Rab VR lite is the equivalent - 250gm, small coke can size - lighter than the original VR but not as robust or warm.
The original VR - or Buffalo equivalent - is good for grovelling up chimneys, iced up or otherwise - but a quite heavy for proper rock climbing. You wouldn't tow one up Positron. In any case, a separate light fleece or thick thermal plus windproof as above has more temperature flexibility in my view.
If it is going to be a bit cold, or your crag is quite big like El Cap. or St John's Head, you want a thin synthetic like the dead bird thing above. I've got a MEC version that's even better <300gm and squashes down to about a pint. It's brilliant, warm, fairly windproof and still small enough to carry on your harness.
When your big crag suffers from afternoon thunderstorms like the Tre Cima, I've climbed in a proper waterproof. Modern thin Goretex or Neo whatsit is light and not sweaty. Tears easily and expensively, so not an everyday choice.
