I agree completely...it sounds like the sippy has become a prop. I would doubt it is so much hunger at night as it is a habit or familiar night routine that she is now used to. I say this because she is only taking 4 oz. diluted, which as the PP mentioned is not much nutritionally. Also, she is 13 months, and really only needs 16-18 oz of milk per day (including milk products) and nothing at night.
The best way to address this issue is to be consistent. You can either continue to water down the milk every few days until it is just water and then nothing, or you can go to nothing right now. IMHO you would be better off just going straight to nothing, as at 13 months trying to slowly water it down could just lead to a long drawn out process. Also,I'm sure she is very aware and bright at 13 months, and at some point she is going to realize what is going on and resist. So why not just deal with the resistance now? I know you mentioned in a previous post that you hate to see her miss sleep over just an ounce or two of milk, but if you think long term, waking every night for the milk is more detrimental to a good night's sleep that a week or two of training so that she sleeps through every night (minus the normal brief wakings that all toddlers have of course)
If she wakes in the night I would not offer the sippy, or even have it anywhere in sight. If she is just whining I would leave her be. If it turns into outright crying you can use one of Tracey's methods to provide support while allowing her to fall back asleep on her own. I know that it can be very difficult, she may even be up for hours the first few nights, but if you consistently do this for 1-2 weeks you will likely see a real improvement! Just remember that she is used to one way of doing things, and at 13 months she will resist, and resist strongly at first, so you just need to be willing to really give it a chance to work. I think you will be pleasantly surprised! HTH