The Hebrew root בלג appears five times in תנ”ך.

ירמיהו ח:יח
מַבְלִ֥יגִיתִ֖י עֲלֵ֣י יָג֑וֹן עָלַ֖י לִבִּ֥י דַוָּֽי:

עמוס ה:ט
הַמַּבְלִ֥יג שֹׁ֖ד עַל־עָ֑ז וְשֹׁ֖ד עַל־מִבְצָ֥ר יָבֽוֹא:

תהלים לט:יד
הָשַׁ֣ע מִמֶּ֣נִּי וְאַבְלִ֑יגָה בְּטֶ֖רֶם אֵלֵ֣ךְ וְאֵינֶֽנִּי:

איוב ט:כז
אִם־אָ֭מְרִי אֶשְׁכְּחָ֣ה שִׂיחִ֑י אֶעֶזְבָ֖ה פָנַ֣י וְאַבְלִֽיגָה:

איוב י:כ
הֲלֹא־מְעַ֣ט יָמַ֣י יחדל וַחֲדָ֑ל ישית וְשִׁ֥ית מִ֝מֶּ֗נִּי וְאַבְלִ֥יגָה מְּעָֽט:

HALOT connects the word to the Arabic balaja, to break (dawn) and balija, to be cheerful, happy.

This does not make sense in the verse in Jeremiah.  HALOT has a separate entry for מבליגיתי, where the text is emended to מבליגית or מבלי גהה, meaning “without healing” – which accords with the Greek, but is still difficult.

My new favorite website, net.bible.org, has:

⁴⁶ tn The meaning of this word is uncertain. The translation is based on the redivision and repointing of a word that occurs only here in the MT and whose pattern of formation is unparalleled in the Hebrew Bible. The MT reads מַבְלִיגִיתִי (mavligiti) which BDB provisionally derives from a verb root meaning “to gleam” or “to shine.” However, BDB notes that the text is dubious (cf. BDB 114 s.v.מַבְלִיגִית). The text is commonly emended to מִבְּלִי גְּהֹת (mibbÿli gÿhot) which is a Qal infinitive from a verb meaning “to heal” preceded by a compound negative “for lack of, to be at a loss for” (cf., e.g.,HALOT 514 s.v. מַבְלִיגִית and 174 s.v. גּהה). This reading is supported by the Greek text which has an adjective meaning “incurable,” which is, however, connected with the preceding verse, i.e., “they will bite you incurably.”