From BiblePortal Wikipedia

Hastings' Dictionary of the New Testament [1]

Two words are so translated-μεγαλειότης and μεγαλωσύνη. According to formation (the first from μεγαλεῖος = ‘stately,’ ‘magnificent’; the second from μεγαλο- = ‘great’) they denote respectively the appearance and the fact of greatness, regal state, and regal might. On the whole, the distinction holds good in usage.

1 . μεγαλειότης, ‘magnificence,’ is applied to Solomon (1  Ezra 1:5), and in the NT (by Demetrius, the silversmith) to the Ephesian Artemis ( Acts 19:27). In  2 Peter 1:16 it is used of Christ’s transfiguration-glory on the mountain-top, and, with interesting coincidence, in  Luke 9:43 of the manifestation of Divine power in His healing of the demoniac boy at the mountain-foot (cf. Clement, Ep. ad Cor. xxiv., Ign. ad Rom. i.; τὰ μεγαλεῖα τοῦ θεοῦ,  Acts 2:11).

2 . μεγαλωσύνη is used in the Septuagintas the translation of נְּדֽלָּח or נּדָל. It is applied to David ( 2 Samuel 7:21) and to the kings of the earth ( Daniel 7:27); elsewhere to the sovereign greatness of God ( Deuteronomy 32:3,  1 Chronicles 29:11,  Psalms 145:3;  Psalms 145:6, etc.). From the Septuagintit has passed into the vocabulary of Hellenistic Judaism ( e.g. Book of Enoch , v. 4, xii. 3, xiv. 16), of the NT, and the Apostolic Fathers (Clement, Ep. ad Cor. xx., xxvii., lviii., lxi., lxiv.). In  Hebrews 1:3 ‘the Majesty on high,’ and in  Hebrews 8:1 ‘the Majesty in the heavens,’ is equivalent to God Himself in His heavenly dominion (cf. Book of Enoch , v. 4, ‘ye spake hard words … against His Majesty’; Clement, Ep. ad Cor. xxvii., ‘by the word of His Majesty all things were framed together’). Most frequently it is used in doxology ( Judges 1:25,  1 Chronicles 29:11; Clement, Ep. ad Cor. xx., lxi., lxiv.).

Robert Law.

Vine's Expository Dictionary of NT Words [2]

1: Μεγαλειότης (Strong'S #3168 — Noun Feminine — megaleiotes — meg-al-i-ot'-ace )

see Magnificence.

2: Μεγαλωσύνη (Strong'S #3172 — Noun Feminine — megalosune — meg-al-o-soo'-nay )

from megas, "great," denotes "greatness, majesty;" it is used of God the Father, signifying His greatness and dignity, in  Hebrews 1:3 , "the Majesty (on high)," and  Hebrews 8:1 , "the Majesty (in the Heavens);" and in an ascription of praise acknowledging the attributes of God in  Jude 1:25 .

King James Dictionary [3]

MAJ'ESTY, n. L. majestas, from the root of magis, major, more, greater.

1. Greatness of appearance dignity grandeur dignity of aspect or manner the quality or state of a person or thing which inspires awe or reverence in the beholder applied with peculiar propriety to God and his works.

Jehovah reigneth he is clothed with majesty.  Psalms 93

The voice of Jehovah is full of majesty.  Psalms 29

It is applied to the dignity, pomp and splendor of earthly princes.

When he showed the riches of his glorious kingdom--the honor of his excellent majesty many days--  Esther 1

2. Dignity elevation of manner.

The first in loftiness of thought surpass'd,

The next in majesty--

3. A title of emperors, kings and queens as most royal majesty may it please your majesty. In this sense, it admits of the plural as, their majesties attended the concert.

Webster's Dictionary [4]

(1): ( n.) Hence, used with the possessive pronoun, the title of an emperor, king or queen; - in this sense taking a plural; as, their majesties attended the concert.

(2): ( n.) Dignity; elevation of manner or style.

(3): ( n.) The dignity and authority of sovereign power; quality or state which inspires awe or reverence; grandeur; exalted dignity, whether proceeding from rank, character, or bearing; imposing loftiness; stateliness; - usually applied to the rank and dignity of sovereigns.

Baker's Evangelical Dictionary of Biblical Theology [5]

See Glory