I would guess that the protein being over-expressed is toxic to the cells and therefore some of them dye. This could be either direct toxicity or due to the over-expression (for example, over-expression of E. coli membrane proteins in E. coli can be a burden on the cells). If this become an issue try lowering the concentration of the expression inducer (assuming you indeed use an induced system).
I agree with Yoram. It doesnt have to be really "toxic" meaining killing the cells, it might just to slow them down. The non-induced culture will grow faster and thus also the OD will increase faster. It would also help if you could be more specific in terms of what cells are you using, what inducer system and about duration of the expression upon induction. All the best Tomas
I agree with Tomas, your question is rather ambiguous. If what you mean is that the induced cells have wet weights -or what have you- in the same ballpark as the uninduced cells, but significantly different OD, rembember that OD is influenced by cell shape, which may change upon expression.