Breast Tissue and Fat Weigh the Same?

Fat volume for volume weighs about 80% of water. Breast tissue is closer water than it is to fat. Therefore it is my rough estimate that fat is probably somewhere in the 80-85% of the density of breast tissue.
I assume you are referring to liposuction when it comes to breast reduction. Also remember that the volume of aspirated material is not all fat. Depending on the situation, my measurements have shown that anywhere from 60-80% of the material removed is fat. Therefore you must aspirate about 650-875cc of tissue to equal 500cc of removed fat which will weigh about 400gms.
For example in the wikipedia patient below, I removed 900 cc of aspirate.

Breast tissue is generally more dense than fat and therefore heavier. It is really hard to predict how much breast tissue will weigh when removed and it is impossible to guarantee a postoperative breast size. My general approach is to ask a patient whether they want to be left on the full side or whether they want to be as small as possible while still having pretty breasts. There are some times that it is clear that more than 500 gms will be removed, particularly when the breasts are really large. If your breasts are smaller, it is not possible to predict and guarantee a resection weight of 500 grams.

Unfortunately, there is no direct correlation between the amount of tissue removed and the ultimate cup size that a patient will wear after breast reduction surgery.

I often suggest a patient's that they should have as much tissue removed as possible while  retaining proportionality with the remainder of your torso.  

Before undergoing the breast reduction procedure it is very important to communicate your size goals with your surgeon.  In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as “natural” or “C cup” or "fake looking" means different things to different people and therefore prove unhelpful.
Also, as you know, cup size varies depending on who makes the bra; therefore, discussing desired cup  size may also be inaccurate.

Best wishes.

Usually breast parenchymal tissue is firmer and heavier than fat in the breast...but grams are grams so 500 grams of fat will weight exactly the same as 500 gms of parenchyma. When performing a breast reduction, you will have components of both in the specimen removed. Most patients that I treat for symptomatic macromastia are like you, they still want a reasonably sized breast to be in proportion with the rest of their body. I usually keep them in the large C or D range. If they are really large to begin with, they may even end up to be a bit larger than a D.

Breast tissue will generally weigh more than pure fat because it contains not only fat but breast tissue itself. We cannot tell you what size you might be without seeing you. Only you and your plastic surgeon can get some idea of final size and even then it will never be a precise prediction.

I am not quite sure what difference would the differential weight of breast skin, breast gland and breast fat have in your decision to have a presumably medical insurance paid Breast Reduction.
It SOUNDS like your insurance MANDATES the removal of at least 500 grams (1.1 pouds) from each breast. This means that unless your surgeon removes this amount of weight fro each breast - your breast reduction operation may be considered a cosmetic Breast Lift (Mastopexy) by your insurer and you may become fully liable for its entire cost.
It is very hard to predict post-operative cup sizes based either on breast implant volume placed in the breast OR from breast tissue (including fat) removed from the breast.
If you are NOT willing to risk smaller breasts, you should not have the surgery through your insurer. Instead, pay for it yourself and ask your surgeon to remove LESS than 500 grams to get the breast size YOU want.

For equal volumes of tissue, breast tissue weighs more than fat. Without seeing photos of you or examining you, I can't say anything about what size you will be after a 500 gram reduction. And really, neither can your surgeon because cup size predictions are never completely accurate.
Alternatively, you could have less reduction done and a better cosmetic result but you might fall short of insurablilty and need to pay for this out of pocket. But wouldn't this be better than destroying your breast aesthetics?