It's accepted. You're right that it's a very good translation, we just put 'satisfied' to avoid ambiguity. We mean content (also an accepted answer), not so pleased that you're more or less starting to feel smug about it, and not 'happy' as in 'overjoyed'.
It's the same distinction. Scientifically, we use massa to denote the amount of matter (mass), and tyngd is the gravitational pull (weight). But for everyday purposes, the two - and vikt - are used interchangeably, just like in English.