The term "mass" is an intrinsic property of any body, and doesn't depend on external factors. The term "weight" is a force, i.e. it measures how much a mass is accelerated. Your mass is $m = 65\,\mathrm{kg}$. Your weight on Earth, which accelerates you at $g = 9.8\,\mathrm{m}\,\mathrm{s}^{-2}$, is
$$
w \equiv mg = 65\,\mathrm{kg}\times 9.8\,\mathrm{m}\,\mathrm{s}^{-2} = 637\,\mathrm{N}.
$$
Similarly, your weight on the Moon is $65\,\mathrm{kg}\times 1.6\,\mathrm{m}\,\mathrm{s}^{-2} = 104\,\mathrm{N}$, and in deep space it's $65\,\mathrm{kg}\times 0\,\mathrm{m}\,\mathrm{s}^{-2} = 0\,\mathrm{N}$, i.e. you're weightless.
Because any acceleration gives you weight, you don't need a massive planet; if you want to visit the ISS, the acceleration of your spacecraft (reaching $29\,\mathrm{m}\,\mathrm{s}^{-2}$, according to NASA) makes you weigh $1950\,\mathrm{N}$ at liftoff, in addition to the $637\,\mathrm{N}$ that Earth makes you weigh. When you get to the ISS, Earth's gravity isn't much weaker than at the ground. There, $g=8.7\,\mathrm{m}\,\mathrm{s}^{-2}$, so if it were hovering above Earth, you'd weigh $565\,\mathrm{N}$. However, since the ISS is in free fall around the Earth, your acceleration with respect to the ISS is $0\,\mathrm{m}\,\mathrm{s}^{-2}$, and you're weightless.
So technically, saying "I weigh 65 kg" is wrong. Instead you should say "My mass is 65 kg". But don't do that. It'll only get you in trouble.