How to lift heavy?

I'm female, very new to any strength exercises. I've read a lot of advices to keep "lifting heavy" to reduce fats. I understand the theory. FYI, i'm petite at 155cm (around 5"1').

Got myself a dumbbell last month, but couldn't seem to be able to lift more than 6lbs. I've also tried gym (trying to pull weighted bands, not sure what it's called), and I can only go as far as 7.5lbs, 4 reps.

How do I progress to lift heavier? Already tried this for a month and no progress. Advise, please.

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