It is worth noting that the adaptation of the heart to weight training is different to the adaptation caused by traditional "cardio".
Weight training causes the heart walls to thicken because, during muscular contraction, blood pressure spikes and the heart must beat against that pressure. For heavy compound exercises the spike can be very high (which is why weight training is contraindicated for some trainees).
Cardio training however is aerobic -- the muscles begin to use blood-borne glucose and oxygen. This means that the heart must deliver more blood per stroke and so ultimately, the heart chambers grow larger.
Both adaptations have a positive impact on heart health. For most people doing both strength and some conditioning work is good.