Ok. Here are my thoughts. Apparently, there is a decent amount of searches for "big eyes". The wordtracker per day says 146. The OVT per month is about 1300. However, the new kick ass google keywords tool says 27,000 searches a month. So.... the domain DOES have some value.
However, due to the nature of the domain, it would be pretty difficult to monetize. There are relatively not many paying advertisers for these keywords. What i do to check this is type "big eyes" into google in quotes and see if any advertisers pop up on the left or top. For these keywords, there isn't one advertiser.And since the domain isn't specific to a retail product or service, there is little hope for affiliate revenue.
Still though, since it does have keywords that are searched in a moderate amount, I would value it at probably $20-40 to the right buyer.