The mini-pill is a progestin-only form of birth control. A combined pill provides both progestin and estrogen, rather than just progestin. Because of this, combined pills are more user-friendly as they are somewhat stronger (in a sense) and work in a slightly different way.

But you are correct, it is risky for a person over 70 kg to rely on the mini-pill to prevent pregnancy. This is because the hormones in the mini-pill may not be strong enough for your body to suppress ovulation and thicken the cervical mucus.

I am not sure why your GP did not want you to consider the regular combined pill. I think the combined pill is a much better option than the mini-pill, and, to the best of my knowledge, your weight would not restrict its use.