Animal

[yashvirsingh]

which animal weeps while eating

[Richard Head]

The mardyarsed Moose. (It's a very rare breed)

[woofgang]

I believe the crocodile

[woofgang]

http://www.worldwidewords.org/qa/qa-cro1.htm

[londondave]

Babies being forced fed

[Yinzer]

I'd say the crocodile, hence the saying "crocodile tears" suggesting that a person is being insincere.