The main celebration was held overnight into Friday.
Those who finish their prayers leave the site to make room for more arrivals, with an estimated total of around 3,000 expected this week.
Some 500 Jews plan to remain in Leżajsk for the Sabbath, which begins on Friday evening.
The prayers at Weisblum's tomb last two to three hours.
Hasidic Jews believe that a person's soul returns to the place of his or her burial on the anniversary of their death. They visit Weisblum's grave in Leżajsk to ask his spirit to help them with important life issues, such as health and prosperity in business and family.
All requests are written down on small pieces of paper, which are then placed on the grave. After the prayers, which are accompanied by traditional dances and the singing of psalms, Jews eat a kosher meal consisting of beef, fish, eggs, fruit and vegetables.
In late March, thousands more Jewish pilgrims are expected to gather in Leżajsk for additional remembrance ceremonies, with their numbers potentially reaching 15,000.
Weisblum was one of the founders of the Hasidic movement, whose aim was to revive Judaism in the 18th century. He gained a reputation as a healer of souls and bodies.
Before World War II, Leżajsk had a sizeable Jewish population and was among the most important centres of the Hasidic movement in Poland. The tradition of the annual prayers at Weisblum's tomb was revived in the 1970s.
(mk/gs)