Here is what Alford put in his apparatus regarding this phrase. Alford's original in my Logos edition is filled with abbreviations, I replaced some of the less common abbreviations with the expansions for some of the references that you get by hovering over a text here. Finally for the significant manuscripts I left the standard abbreviation (like ABC in the omit section):
aft γεννωμενον ins εκ σου (prob a particularizing addition,—see Matt 1:16: Gal 4:4: so Mey) The CODEX EPHRAEMI 1. 33; the Vulgate version (A.D. 383) (with gat per); Codex Vercellensis, fourth century; Codex Colbertinus, eleventh century; Codex Palatinus Vindobonensis, fourth (or fifth) century; the Peschito (or simple) Syriac version; the Æthiopic version. Assigned to the fourth century; the Armenian version. Made in the fifth century; Protev-5-mss; [Val(in Hipp)] Dialexpr Thaum2; Athanasius, Bp. of Alexandria, 326–373; Epiph1 Ephr [Amphilochius, Bp. of Iconium, 374]; Chr Thdrt Damasc1; Irenæus, Bp. of Lyons, 178; Tertullian, 200; Cyprian, Bp. of Carthage, 248–258; Hilary, Bp. of Poictiers, 354–368; Gaud; Jerome, fl. 378–420.
According to Alford these Manuscripts and lectionaries omit the reading:
ABC3Dא; Amiatinus, written about 541; Codex Veronensis, fourth or fifth century; Codex Brixianus, about sixth century; Codices Corbeienses (very ancient); Codices Sangermanenses (very ancient); Codex Rhedigerianus, about seventh century; the later or Philoxenian version; he Jerusalem Syriac Lectionary; the Coptic or Memphitic Egyptian version; the Gothic version; the Armenian version. Made in the fifth century; Protev-6-mss Dion Petr; Eusebius, Bp. of Cæsarea, 315–320; [Cyr-jer1 Cyr2]; Orig-int1; Tertullian, 200
Henry Alford, Alford’s Greek Testament: An Exegetical and Critical Commentary (Grand Rapids, MI: Guardian Press, 1976), 447.
Here is what Metzger says on his commentary for the UBS4
The words ἐκ σοῦ are apparently an early addition prompted by a desire for greater symmetry after the two preceding instances of the second person pronoun. The expanded reading gained wide currency in the early church through Tatian’s Diatessaron. The reading ܒܟܝ (literally “in thee”), for which Dionysius Barsalibi (died A.D. 1171) argues vigorously in his commentary on Luke,1 is read by the earliest manuscripts of the Peshitta (the Curetonian and Sinaitic Syriac manuscripts are not extant here) and is adopted as the text in Pusey and Gwilliam’s critical edition
Bruce Manning Metzger, United Bible Societies, A Textual Commentary on the Greek New Testament, Second Edition a Companion Volume to the United Bible Societies’ Greek New Testament (4th Rev. Ed.) (London; New York: United Bible Societies, 1994), 108.
As to why Beza may have included it I can't be certain of anything. Perhaps Beza was influenced by the fact that this reading had survived through the Vulgate.
Being curious I looked this up in the various editions of the Greek text that I have to see which ones contain this reading. Even among various Textus Receptus versions it is in some and removed in others. Both Stephens (1550) and Elzevir (1624) omit the reading. Beza's version includes it and so does Scriveners (1894) version, but Scrivener's version is just a modification of Beza's version and not a start from scratch version of the TR. Both Robinson's Byzantine majority text form (2005) and the UBS4 text also omit the reading.
Given the early age of some of the commentaries and the Peshitta (150) version including this reading, it may actually be one of those rare cases where the original was preserved in a very small number of manuscripts. Another controversial example of that type is the famous Johannine comma in 1 John 5:7–8. Like this one I favor the inclusion of the comma as being original, in spite of the very small number of manuscripts.