There are various ways of say them:
to be skinny
やせている (the most common)、細い、スリムな、etc
*引き締まっている/引き締まった is used for "to be slim and muscular".
to be fat
太っている (the most common)、ポッチャリしている (sounds a bit cute)、恰幅が良い (mainly for men)、貫禄がある、etc
*We don't say ふくぶくしい, at least I don't. 体格が良い is also used for "to be muscular".
**There also are some insults that I didn't write.
I hope this helps you.