Unless you do circuit training, weight training has little direct affect on the heart rate. Weight training is anaerobic exercise. It is aerobic exercise like walking or running that has a direct affect on the heart rate because it strengthens the heart. Weight training does not.
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It actually has very little effect. Weight training can temporarily raise your blood pressure, but it will not do much to condition your heart. If you are concerned about it, ask your personal physician whether weight training would be right for you.