What is claimed is:1. A suspension board with circuit comprising:a metal supporting board, a base insulating layer disposed at one side in a thickness direction of the metal supporting board, and a conductor layer disposed at one side in the thickness direction of the base insulating layer and including a connecting terminal electrically connected to a slider, wherein:the base insulating layer includes a first base insulating layer disposed at the one side in the thickness direction of the metal supporting board and a second base insulating layer covering the first base insulating layer and disposed at the one side in the thickness direction of the metal supporting board,the base insulating layer has a terminal region, when projected in the thickness direction, overlapped with at least the connecting terminal and a circumferential region not overlapped with the terminal region and around the terminal region,in an entire region of the base insulating layer, the conductor layer is not located between the first base insulating layer and the second base insulating layer, andthe thickness of the terminal region is thicker than that of the circumferential region.2. The suspension board with circuit according to claim 1, whereinthe terminal region includesa first terminal region-insulating layer made of the first base insulating layer and disposed at the one side in the thickness direction of the metal supporting board anda second terminal region-insulating layer made of the second base insulating layer and disposed at one side in the thickness direction of the first terminal region-insulating layer; andthe circumferential region includes at least a second circumferential region-insulating layer made of the second base insulating layer and disposed at the one side in the thickness direction of the metal supporting board.3. The suspension board with circuit according to claim 2 further comprising:a cover insulating layer covering the conductor layer so as to expose the connecting terminal and disposed at the one side in the thickness direction of the base insulating layer and a pedestal supporting the slider, whereinthe pedestal includesa first base pedestal layer made of the first base insulating layer and disposed at the one side in the thickness direction of the metal supporting board,a second base pedestal layer made of the second base insulating layer and disposed at one side in the thickness direction of the first base pedestal layer, anda cover pedestal layer made of the cover insulating layer and disposed at one side in the thickness direction of the second base pedestal layer.4. The suspension board with circuit according to claim 1, whereinthe terminal region includesa first terminal region-insulating layer made of the first base insulating layer and disposed at the one side in the thickness direction of the metal supporting board anda second terminal region-insulating layer made of the second base insulating layer and disposed at one side in the thickness direction of the first terminal region-insulating layer; andthe circumferential region includes at least a first circumferential region-insulating layer made of the first base insulating layer and disposed at the one side in the thickness direction of the metal supporting board.5. The suspension board with circuit according to claim 4 further comprising:a cover insulating layer covering the conductor layer so as to expose the connecting terminal and disposed at the one side in the thickness direction of the base insulating layer and a pedestal supporting the slider, whereinthe pedestal includesa first base pedestal layer made of the first base insulating layer and disposed at the one side in the thickness direction of the metal supporting board,a second base pedestal layer made of the second base insulating layer and disposed at one side in the thickness direction of the first base pedestal layer, anda cover pedestal layer made of the cover insulating layer and disposed at one side in the thickness direction of the second base pedestal layer.