Partial ionisation in water
A carboxylic acid is weak because only some acid molecules ionise in water. The ionisation is reversible: CH3COOH ⇌ H+ + CH3COO−. Many undissociated acid molecules remain in solution. Weak does not mean that no hydrogen ions form, and it does not mean that the substance is necessarily dilute. Strength describes the extent of ionisation, not the amount dissolved per unit volume.