גלל

Abarim Publications' online Biblical Hebrew Dictionary

גלל גיל

None of the consulted sources mentions anything about a relation between the roots גלל (galal) and גיל (gil), but their forms are quite obviously related and their meanings are similar as well:

גלל I

The verb גלל (galal I) is all about rolling; it means to roll some object on, upon or away. In a figurative sense it is used in ideas like to whirl or dazzle and even to roll oneself onto the Lord, meaning to put one's trust in him (Psalm 22:8) or to commit oneself to him (Psalm 37:5, Proverbs 16:3). When this verb is used for physically rolling something away or somewhere else, the object is usually stones (Genesis 29:3, Joshua 10:18).

This verb's enormous array of derivations:

The masculine noun גל (gal), meaning heap or pile (Joshua 7:26), a heap of ruins (Isaiah 25:2), or, in case of water: wave or billow (Jeremiah 5:22).
The masculine noun גיל (gel), meaning dung (Job 20:7, Ezekiel 4:12).
The feminine noun גלה (gulla), meaning bowl, basin or spring (Joshua 15:19, Zechariah 4:2). Note that this noun is spelled the same as the verb גלה (gala).
The masculine noun גלל (galal), meaning dung (1 Kings 14:10).
Scholars assume the existence of adjective גליל (galil), meaning turning or folding, to explain the statement made in 1 Kings 6:34, that two "leaves" of a door were turning or folding. Here at Abarim Publications we don't agree that the text speaks of a door's leaves, but read our article on the root צלע (sl') for the details. We believe that this word is the same as the (obviously) identical masculine noun: גליל (galil), denoting a supporting cylinder or rod (Esther 1:6), ring (Song of Solomon 5:14). Note that this word is also identical to the Hebrew version of the name Galilee (Joshua 20:7, 1 Kings 9:11, Isaiah 9:1).
The previous noun made feminine: גלילה (gelila), meaning circuit, boundary or territory (Joshua 4:4, Ezekiel 47:8).
The noun גלול (gillul), meaning idols (Ezekiel 22:3, 1 Kings 15:12). This word occurs only in plural. Scholars can't decide whether this noun came from the idols' shapes (round/curvy?) or whether they were considered "dung-things" or crap, so to speak.
The masculine noun גלגל (galgal), meaning wheel (Isaiah 5:28) or whirlwind (Psalm 77:18).
The masculine noun גלגל (gilgal), meaning wheel (Isaiah 28:28 only).
The feminine noun גלגלת (gulgoleth), meaning skull or head. Note that the noun פנים (panim), meaning face, comes from the verb פנה (pana), meaning to turn. Also note that in Biblical times the head did not hold the same regard as it does to us today. To us the image of a skull represents death or danger, but that symbolism is not Biblical. In Biblical times, the head was also not regarded as the seat of the mind or the intellect, but rather as the most public part of the body, comparable with the door of a house or city. The head was seen as the seat of individual personality, or rather a person's public profile. It was the part of a person with which that person engaged others and the world around him. One consumed food via the head, listened to others, spoke to others and viewed others, but the head was not seen as a repository or reservoir of anything. Our word occurs a mere 13 times in the Bible, half of which in the context of literally a head- (skull-) count (Exodus 38:26, Numbers 1:2, 1 Chronicles 23:13). In Exodus 16:16, the Israelites are commanded to gather one omer of manna per "skull" (something similar occurs in Exodus 38:26 and Numbers 3:47). In Judges 9:53, a certain woman drops a mill stone on Abimelech's head, thus crushing his skull and with it his personhood, in 2 Kings 9:35 we find what's left of Jezebel after the dogs are done with her: her hands and feet and her skull, and in 1 Chronicles 10:10 Saul's skull ends up in the temple of Dagon. Note that all gospels emphasize that Jesus died on Golgotha (or Calvary in Luke, which means the same), which is obviously highly significant when one realizes that the name Golgotha comes from our word גלגלת (gulgoleth), and what that word meant to the gospel's audience.
The feminine noun מגלה (megilla), meaning scroll (Jeremiah 36:28, Ezekiel 3:1).

גלל II

There's a second verb גלל (galal), which doesn't occur in the Bible, but in cognate languages it means to be great in rank. Its sole derivative is the masculine noun גלל (galal), meaning account, which with little effort could be attached to the above word group in that an account is both a heap of facts and a bordered "region" of the greater world of events at large. This word only occurs in conjunction with the preposition ב (be), meaning in, to form the meaning of "on account of" (Genesis 39:5, Jeremiah 11:17).

גיל

The verb גיל (gil) yields words that have to do with a circular motion, usually expressing joy or celebration (Isaiah 65:19; Psalm 21:1). It "most often refers to rejoicing at God's works or attributes," says HAW Theological Wordbook of the Old Testament.

The derivations of this verb are:

The masculine noun גיל (gil), meaning rejoicing (Psalm 45:16, Isaiah 16:10).
The feminine noun גילה (gila), also meaning rejoicing (Isaiah 65:18).
The masculine noun גיל (gil), meaning a circle or age. The phrase בן גילו (ben gilu) literally means 'son of circle' and denotes someone born at the same time, contemporary.