be-set' (euperistatos): The most common sense of this word is "to surround." This is the thought in Ps 139:5, and teaches the omnipresence of God. Often wicked men find that the things which they have done so envelope them that they cannot escape ruin (Ho 7:2). The reference in Heb 12:1 is first of all against the sin of apostasy against which repeated warning is given in this book. But the warning is also against any sin that is especially dangerous to us. It, again and again, surrounds us like a besieging army. To surrender would be traitorous and disgraceful, since the Captain of the Lord's host is with us.
⇒See the definition of beset in the KJV Dictionary
Jacob W. Kapp