I'm selling different quantities of the same product, like 1 kg, 2 kg, etc. How can I display a drop-down on the product page to provide an option to the user to select the weight of the product which he wants to buy?

To provide options like weight drop down or size drop down to the user, the user will have to select the variant of the product. For this you will have to provide variants in that product.

Please refer the following topic for more details on Options & Variants:
https://help.storehippo.com/topic/options-and-variants