Don't want to powerlevel on how I know this (but I'll say it's NOT from attempting to cancel my own Life Magazine subscription), but no. The rope doesn't need to be strong enough to hold her weight; just strong enough that her cervical spine - neck vertabrae - snaps first). Also, many have botched their hangings and slowly suffocated themselves/crushed their larynx instead of snapping their neck and severing their spinal cord. Pretty gruesome. Overdoses on over the counter pain relievers are not dependant on weight. ASA ("Asprin") rots out your stomach lining. Once that happens, your stomach acids can eat through your stomach and leak out into your torso, slowly liquifying your organs. (People also do this by drinking small amounts of bleach). Ibuprofin ("Advil") and Acetaminophin ("Tylenol") destroy your liver. Being Deathstar fat doesn't give you a thicker stomach lining or a more robust liver (it can actually give you the opposite), so there are no calculations based on mass. Little kids have been successful in their attempts. Amber is intelligent enough to succeed.
Don't let this bounce around in your mind too much (especially the kid part), or it will mess with you. Instead, look at these totally adorable (and completely off topic) pictures I found!!
