What is the difference between weight and heft?

There’s a dictionary saying heft means weight, but what does heft mean in the phrase of “weight and heft”? Is it "weight and weight"? I think there might be some difference between weight and heft, but I don’t know for sure. I’d be happy if you could help me.

While 'weight' is defined as the downward force on an object due to gravity, heft, in the context of your question, has a more subjective connotation usually involving the "feel" of the object in the hand- 'Hefting' an object usually involves picking up an object and making small motions with it to determine how it feels in the hand. The more flimsy an object feels the less heft it is perceived to have.

A manufacturer will assess the weight of an axe before production.

A psychopath will assess the heft of an axe before a rampage.