I am trying to find out how the Jewish high priests were able to get through the very thick and heavy veil to enter the holy of holies part of their temples?

A curtain separated the Most Holy from the Holy (the outer room).
The high priest entered the Most Holy only on the annual Day of Atonement; at no time could any other person go beyond the curtain that hung between this room and the Holy Place. (Leviticus 16:2)
In the Most Holy the high priest was surrounded by the colorful embroidered cherubs on the tabernacle’s inner covering and on the curtain. (Ex 26:1, 31, 33)
The curtain must have been like a stage curtain that would allow one to pass through as the high priest would need to enter the Most Holy only on the annual Day of Atonement.

At the time of Jesus’ death God expressed his anger by causing the thick, heavy curtain that separated the Most Holy from the Holy Place to be ripped in two from top to bottom. The priests who were carrying on their work in the Holy Place were then able to see into the Most Holy and to have impressed upon them the fact that this compartment contained no Ark representing God’s presence with them. This action by God confirmed that the atonement sacrifices offered by the Jewish high priest were now no longer of value and there was no need for the services of the Levitical priesthood anymore.

See Matthew 27:51; 23:38; and Hebrews 9:1-15.

The curtain was of one piece three inches or more thick - hung from the top to the bottom. The High Priest entered at the side.

They didn't go in. Only the high priest did, only once a year, so it wasn't that big of an issue.

The same way they're doing it in Gaza right now with white phosphorus incendiary bombs