The lightest 2HP is/was the Evinrude or Johnson (same engine just different branding) 2 cycle - at about 18lb.
These old 2 cycle OB engines are virtually indestructible and can still be found ebay, etc.
The reason for the light weight is NO transmission, just precisely tune the low speed jet so that the idle speed is minimal or 'just enough' to keep the engine barely ticking. All the carb adjustments for the low speed and high speed jets are conveniently on the face plate - for convenience and easy access. If looking for a good old one, seek out one from the mid 1980s or later; do change out the water pump for a modern one - a retroifit 'insert' into the old water pump casting is available. All parts are still readily available from Bombardier or their USA outboard parts distributors.
Vintage Evinrude 2 HP Horsepower Horse Boat Motor EXC Original Paint on Prop | eBay