assuming you have not played withthe color options in the settings, the grey dims are driven dimensions, and the black ones are driving. they will both print black - especially if you set it to print in black and white.
you can control the colors in many ways
1. you can change the system options for the color display of the dimensions
2. you can adda layer to the drawing with a defined color and move/auto-assign the dims to that layer
3. you can be consistant in you dimension creation
4. you can select a dim (or ctrl-select several) and assign any color to them
5. and there are probably other ways
Is your boss viewing these in SolidWorks, or are you printing them out or saving as pdf? As Jeremy mentioned the grey dimesnions indicate that they are driven. If you are printing the drawing make sure you are printing in black and white. If you are saving to pdf click the "Options" button in the Save As dialogue box and then uncheck "Export PDF in color".
If you need to print or save a pdf in color, then you can change the color of the driven dimensions to black. Open System Options, select Colors from the left side, and then find "Dimensions, Non Imported (Driven)" and edit the color to make it black. If you are using a sheet format you probably noticed that those lines are gray too. That is under "Inactive Entities" so you can set that to black too.