Yes, dry weeping eyes are a common side effect of HRT or Premarin. There are more such side effects like thinning skin and runny nose which are not mentioned in the common leaflet that mentions the side effect of this drug. You can use eye coolant or drops to relax your eyes if you are facing this side effect. There are many other side effects of HRT which can cause some serious consequences. HRT increases the risk of endometrial and breast cancer in women if the use of this drug is prolonged. One of the common symptoms is the increase in breast density which makes it difficult to recognise the symptoms of breast cancer. In addition to this, use of HRT also increases the risk of gallbladder disease, blood clots, heart attack or stokes. You may also face nausea and breast pain.