Should I lift heavy?

The answer is no. Heavy lifting is mostly good for your ego and that's it. There is a reason why most top-level athletes use light weights and it's because they are training to produce results and not to impress others.

The exercises in Athlete 20XX when done correctly with the right form and with the lighter weights not only produce better results but also keep your form in check.

The gains in strength and muscle should be better, you will not hurt your joints and you should develop your mobility and stability at a much better rate. Personally, I only use light weights with myself and my clients. Lifting heavy is mostly good for showing off or to test how strong I have become.