I need to make the next case: I have product x with the attribute weight 1KG, 4KG, 6KG Need 1KG price before 87.00 After 69.60 4KG price 150 6KG price before 263.00 After 210.40
If you have fixed weights (e.g., 1KG, 4KG, 6KG, etc.), then you could use Product Attributes with "Price adjustment". Alternatively, if you want pricing by any Quantity / range, use Tier Prices.
(P.S. How can you have "1KG before"? You can't enter fractional quantity)