Nuance of meaning... 12:52 Oct 8, 2008
Although this is one translation suggested in some dictionaries, I don't think it always conveys the same feeling as the original expression.
It's a subtle nuance, but "to have eyes bigger than ones belly" has a certain connotation of deliberately choosing, greedily, a large quantity of food than it ultimately turns out one can eat (or of course, the figurative meaning along the same lines...)
On the other hand, "to bite off more than one can chew" rather suggests (probably inadvertently) committing oneself to a course of action that ultimately one discovers is outside one's capacities.
This is clearly the case in the context as given, where the lady in question had taken on a garden that she ultimately found was too big for her to manage; unless it appears in the wider context, I don't think there is necessarily any implication that the decision to purchase this garden in the first place had any element of 'greed' about it, maybe just that she had over-estimated her own capacities...
Even though the difference is subtle, and maybe not even made in FR, I feel it's important to at least take it into account in any given translation context.
Compare:
"I took on a lot of translation work this week, as I was keen to earn some extra money. But my eyes must have been bigger than my belly, because I found I couldn't get it all finished in time"
...with:
"I rather regretted having agreed to do her a favour and proof-read her latest novel, since already by Chapter 2 I could see I'd bitten off more than I could chew." | 
peer agreement (net): +2
