√(G × mass÷radius) [escape velocity] = v_e × ln(m_0 ÷ m_f) [Tsiolkovsky]
Impossible to tell how much extra mass you need but it's exponential. Adding a unit of v_e [effective exhaust velocity] to escape velocity means you need 2.717 times as much fuel in an ideal rocket.
Earth escape velocity is 11000m/s ignoring atmosphere (which is not ignorable). If the new planet is 6x mass and 2x radius then √3 times escape velocity (about 1.73) would be about 8000m/s extra velocity which is about 3 times a random v_e which means you need about a 25 times bigger rocket. Ignoring the denser atmosphere which makes it even worse.
Don't these estimates assume launching from the surface, fully via rocket? On Earth, having air breathing stages to gradually build up speed, or using other launch mechanisms, isn't worthwhile because rockets are more cost effective here, but those tradeoffs change if you're on a planet with higher gravity and a denser atmosphere.
From the archives ... How much bigger could Earth be before rockets wouldn't work? https://space.stackexchange.com/q/14383 Feb 3, 2024 https://news.ycombinator.com/item?id=39243303
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