I have been trying to extract ARN from VAT but the pellet hasn´t form at the end. I have been using ~25mg of tissue and I´ve seen that many protocols are designed for 100mg of tissue. I don´t have the posibility to buy extraction kits.
in principle it is possible to isolate RNA with TRIzol from relative small amounts of tissue. You might downscale the amount of TRIzol (however this does not only depend on the weight of the tissue but also on the volume). You can also use glykogen to improve RNA precipitation (recommended for small amounts of RNA). The addition of glykogen will also lead to a visible pellet, making it easier to work with the material. For fatty tissue you should also include an additional centrifugation step to get rid of the lipids. However, you might want to check out this article:
Article Human Adipose and Skeletal Muscle Tissue DNA, RNA, and Protein Content
In this article it is shown that the RNA content in adipose tissue is significantly lower than in skeletal muscle tissue - less that 50 ng per 1 mg tissue (in this article they used RNAzol which is pretty similar to TRIzol). This means the total amount of RNA you can extract from 25 mg adipose tissue might be rather low, so I would recommend to dissolve the RNA pellet in a small volume of RNAse free water. Even if you have only a small amount of RNA I would recomment to check your RNA by gel electrophoresis to be sure that the RNA is intact (if you are not doing so already).