Weight was the mass of an individual or object. It could be affected by gravity.
Weight of individuals[]

Harry Mudd's weight
Those whose weights exceeded normal measurements were said to be overweight. (TNG: "The Outrageous Okona"; VOY: "Critical Care")
As of 2266, Harry Mudd weighed 240 pounds. (TOS: "Mudd's Women")
As of 2370, Data weighed 100 kilograms. (TNG: "Inheritance") Of that weight, 26.8 kilos was of tripolymer composites, 11.8 kilos was of molybdenum-cobalt alloy, and 1.3 kilos was bioplast sheeting. (TNG: "The Most Toys")
Kor felt insecure about how heavy he was because he was lighter when he had last seen Dax. (DS9: "Blood Oath")
In 2372, Captain Benjamin Sisko noted that his father Joseph Sisko had lost weight, prompting criticism from Jake Sisko, who reminded him that his doctors had told him to keep his weight up following his having been fitted with an artificial aorta. (DS9: "Homefront")
When the crew of the USS Voyager was trapped in The Void, Kathryn Janeway wondered if they would lose weight due to malnutrition. (VOY: "The Void")
In 2381, Lars Lundy correctly guessed Brad Boimler's weight of "a healthy 61.2 kilos," explaining that, his figure drawing class needed a skeletal boy for their life drawing, before inquiring if he had "ever sat for oil?" (LD: "The Least Dangerous Game")
Weight of objects[]
In 2370, when Jadzia Dax requested a bat'leth from the holosuite, she specified it to weigh five point three kilos. (DS9: "Blood Oath")
In 2378, B'Elanna Torres played The Doctor's holonovel entitled Photons Be Free in the role of an emergency medical technician. Her character's mobile emitter was much heavier and bulkier than the one in reality and she speculated it must have weighed fifty kilos. When she asked The Doctor about it, he said that its weight served as a metaphor for the burden of being a hologram. (VOY: "Author, Author")