If the grout were a day or two old I'd say have at it.

With the grout being several weeks old, your best bet for success would be to clean out the grout joints deeper than they are wide, then regrout. When you regrout over already cured grout, the new grout may not adhere well, or you might get a slight mismatch in color between new and old.

Since this is DIY, you could give it a shot "as is". If the new grout delaminates or powders off, or if any fluctuations in color are unacceptable to you, then you're back to square one...which would be to clean the joints out a bit, then regrout.

Thanks for your input. Will it make a difference if the grout is already sealed?

The grout already seems to have color fluctuations - in both rooms. Any ideas of what contributes to that?

Thanks again...

If there's a sealer, I'd recommend removing the existing.

Color fluctuations are usually due to too much water, either in the mix or during cleanup.