We can commence by deducing for ourselves that these coverings did not all act as "coverings". There are two reasons I say this: 1) Only one covering is needed to achieve the quality of "covering" any given vessel. Additional layers do not add to the state of being "covered". Once something is covered, it remains so until that last layer is removed. 2) The second reason is that the word "beged" (garment) is used in connection with the blue wool, not "kisooy", (cover) as is used with the animal skins.
What is the purpose of having both, blue sheets and animal skins covering the vessels of the Tabernacle when traveling? Why was the order of layers for the Ark; animal skin covered with a blue sheet, whereas the remaining vessels were the opposite i.e., the blue sheet was placed over the vessel first, followed by the animal skin above? If one layer achieves "cover", what is the purpose of a second layer?
The commentators state that the animal skins served to protect the vessels from the elements. But protection is only one reason to cover an object. Another reason is to hide something from visibility. Perhaps, when not together forming the halachik structure of the Tabernacle, the vessels were not functioning in their true purpose. Meaning, the vessels served to compliment the essence of the Tabernacle, I mean the Ark. In "The Temple and Tabernacle" article, I suggested the vessels (aside from the Ark) served to teach man those ideas which are within man's grasp. But this is only taught as these vessels are placed outside the Holy of Holies. It is precisely from this positioning that we derive this idea. The restriction from entering the Holy of Holies where the Ark rested, teaches man that he cannot approach any understanding of G-d in this life. Therefore man's abstention from entering this room demonstrates his inability to approach G-d. The other room, the Holies, where the Menora, Table and Altar are found, represent areas of knowledge which are in fact available to man. Therefore, when the vessels are not in the Tabernacle, and not in proximity to the Holy of Holies, this derivation is not apparent, and perhaps even other man made ideas might be projected onto these impressive, golden vessels when seen. Therefore, an additional blue sheet is placed on these vessels, not for protection against the elements, but as an act of "concealment". Teaching that these vessels have no intrinsic value when not forming the total Tabernacle, where they actualize their purpose, contributing to the structure of the Tabernacle. This is why, (although already protected from the elements via the animal skins) we find the command to cover them with blue sheets. This extra layer is therefore not acting as a protection, but as a veil.
The Ramban says that the blue sheets are meant to remind one of the "essence of the heavens for purity". So what is to be understood by "heavens"? Heavens are euphemistically used to connote the metaphysical or spiritual realm, also the area of knowledge. Although the heavens are no less physical than the Earth, being out of man's reach, and lofty in estimation, Ramban uses the heaven's aura as a metaphor for the spiritual world. So the blue of the sheets is to signify that the Ark and the other vessels partake of leading man towards the true world of knowledge. These are the goals of the vessels. But since the other vessels do not achieve this goal when not assembled in the Tabernacle, even this "spiritual" aspect is hidden, and therefore under the animal skins. The Ark however derives no compliment from the other vessels, and therefore the blue sheet is exposed, teaching that its purpose never diminishes, even when the structure is not in existence.
This concept was discussed in the article "The Ark's Poles".
Mesora: You are right, the blue sheets cannot be 'functioning' as a veil, but they can have the 'purpose' of a veil in concept, to teach that the vessels "should" be covered.