Jin is a measure that's about half a kilo and probably similar to the pound (lb) in English. Think of gongjin as a long pound or kilo. Literally i guess it's the public weight measure.

My teacher told me that they tend to use jin for small amounts and gongjin for more than a couple.

斤 is an old Chinese weight or mass measuring unit. 公 means "public". 公斤 Etymologically is like "the public weight". 公 is used for metric measurements and 英 （short for England) is used for standard/imlerial measurements.