I found some really good information on this website about weightlifting and the singing voice. Some of the responses in this article are very helpful to what you are asking about.
Taking full deep breaths is very important while you are singing. However it is more natural to take shallow breaths, especially while exerting oneself physically. Try breathing deeply, as though you were singing, while you are exercising as well. Also make sure you are not holding your breath while you lift, as that can cause an unfortunate amount of constriction on important parts of your vocal mechanism.
There are certain vocal warm-ups that can loosen up your vocal folds and the surrounding muscle mass, such as a sigh. A sigh sounds like a stereotypical yawn, where you use the vowel "ah", beginning on a high point in your register and descending to the lower part of your register; one could also move from low to high. Another way to insure you are doing this warm-up healthily is to use an "ng" sound (like the end of singiNG) and do the yawn exercise. This creates a healthy environment for your vocal folds.
There are muscles in your upper body that are integral to healthy singing and exercise is a very good way to enhance your ability to do so. Also, exercising can be helpful in increasing breath support. This is all contingent on exercising in a healthy, responsible and beneficial way.
Thank you for asking this question.