Overtraining in weightlifting can lead to hormonal imbalances, particularly an increase in cortisol, the body's stress hormone. Elevated cortisol levels can stimulate the sebaceous glands to produce more oil, leading to clogged pores. When combined with increased sweating and potential bacterial growth on the skin, this can result in acne breakouts.
My recommendation is train a maximum of 3-4 times per week if you're worried about this. (edited)