A character gains a lot of weight in a short time, gaining mass in every part of their body, even their voice. Their voice will get deeper and thicker as if some of the extra pounds ended up in their larynx. Generally only found in animated works, and very common in anime. Not to be confused with the Heavy'svoice. Compare and contrast Power Makes Your Voice Deep.
Lampshaded by Hachibei in chapter 88, page 14 of Ai Kora when he tells Kirino, after she has gained weight due to a drug slipped into the dorm's water supply, that her "voice is fatter". This is a pun in the original Japanese version of the manga, in which Hachibei tells Kirino "koefuto", which can usually mean "to grow fat", but in this context it includes the word "koe" meaning "voice".
In episode six of Wandaba Style, The Professor is in a slump, so his pilots (the girls of Mix Juice), have nothing to do, and thus gain weight from just sitting around. This is hinted at (before we see them completely) by their voices. (Note: averted in the English dub)
In an episode of Wagamama Fairy Mirumo De Pon!, Mirumo and Kaede both gain weight thanks to Kaede's rival sending her cakes. Kaede doesn't gain too much weight, but Mirumo, being a Lilliputian, has a more substantial weight gain with a lowered voice to match.
During an episode of MÄR, the team (specifically, Princess Snow) fights against an ugly little girl whose signature ARM is the Gingerbread House - a house of sweets. Eating it makes her grow to sumo-like proportions, gaining superhuman strength and toughness in the process. And of course, as she grows bigger, her voice grows deeper and thicker. (Also, she turns into a Gonk.)
In the seventh episode of Di Gi Charat, Gema falls in the river and drinks a lot of water, making him grow huge and giving him a deep voice.
Zura from Mamotte! Lollipop is a little seahorse-thing that can blow up like a balloon and float. When it does this, it can still talk, but its voice is much deeper than usual.
This happened to Stocking in episode 4-A, after she balloons into an obese giant.
Samurai Champloo's Fuu gets this whenever she gorges herself in at least the Japanese and English versions of the show (not so much in the German version).
In the second episode of South Park Cartman gains a lot of weight, and his voice gets deeper (and thicker).
It also happened to all of them in "Make Love, Not Warcraft".
Inverted in "Spontaneous Combustion", with Cartman's voice getting higher after losing a lot of weight.
Bender from Futurama may be a robot and thus find it hard to get fat but in one "What if..." episode where he becomes human and then lives as he normally does (which is to excess) he becomes extremely fat with a deeper, less excited voice.
Subverted in one episode of Scaredy Squirrel, where, after gorging on nutbars, Scaredy seems to have a deeper voice, but he just had a (still-wrapped) nutbar in his throat.