The animated illustrations in "Vibration modes of motorcycles"
by Vittore Cossalter, Roberto Lot (posted in the community wiki answer) do a great job of illustrating capsize, weave, and wobble.
Simplified verbal approximations might be:
Capsize - The bicycle moves as if to fall over on its side with no distinct oscillations.
Weave - The bicycle moves with an oscillating pattern as if arcing between cones on a straight path without inducing movement at the handlebars (perhaps subtly more complex because of the perpendicular twisting motions of yaw and roll axes of the entire bicycle object).
Wobble - The bicycle moves distinctly at the front due to twisting movements of the handlebar to turn the front wheel back and forth (isolating twisting motion largely at the fork steering tube axis). To further contrast with weave, the front wheel might arc back and forth between cones on a straight path while the handlebar flops side-to-side but the rear wheel remains largely in place striking each cone.