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.
Typically, I see weight as a noun and heft as a verb (weight being the downward force that is a result of mass and gravity, and is what we feel; heft being the action of lifting an item to test its weight).
As we can see here, the phrase "weight and heft" has become increasingly popular over the past couple decades.
However, we see that when comparing "weight" and "heft", the word "weight" is so much more popular than the word "heft" that it looks as though "heft" is not used at all.
weight: the amount or quantity of heaviness or mass; amount a thing weighs.
heft(n): weight; heaviness (v): to test the weight of by lifting and balancing