The problem with weight lifting is that the VALSALVA situation in your chest, holding your breath so the chest forms a firm brace for the weight, especially in a manuever like a bench press, raises your BP considerably while the excercise is being done.
THis is BAD form.
You can ameliorate the VALSALVA by making sure you EXHALE in the lift portion of the maneuver. Breath OUT during the exertion and IN during recovery (lowering the weight.) The correct way doesn't come naturally and must be consciously learned.
BP unless extremely elevated and uncontrolled should NEVER be a reason to forego the weights. I think that kind of advice usually comes from doctors who have never lifted anything heavier than their checkbooks.

HEavy resistance training should be a part of everyone's life.