A three-tonne restriction has been in place since 2012.
It has been managed previously using width restriction posts to deter overweight vehicles entering the bridge.
But Kensington and Chelsea Council says those who ignore the warnings will get a penalty notice of £130 from next Thursday.
More than 1,400 warning notices have been issued since the 6th of December and regular bridge users have been given advance notice.
In October the Council resurfaced the bridge, spending £100,000 repairing the deck.
The authority says the bridge is currently structurally sound.
But council bosses say they don’t want to be in the same position as Hammersmith Bridge which has been closed to vehicles for 5 years.