Green’s Dictionary of Slang

boost v.1

1. (US) to praise, to extol, esp. one’s own town or city; thus booster, one who makes such promotions.

[US]S. Smith Major Downing (1834) 215: You was the first person that ever give me a lift into public life, and you’ve been boosting me along ever since.
[US]Schele De Vere Americanisms 573: It is only where [...] a casual word happens to strike the fancy of the people with such force as to make a word popular, like ‘boost’ [...] that really new words establish their claim to be considered essential parts of the language.
[US]F. Francis Jr Saddle and Mocassin 121: If you think that I’m trying to boost the place up because it belongs to us [...] call me an old mud-turtle.
[US]Ade Artie (1963) 63: There’s a lot o’ them church people that boosted him two years ago that’s out now to skin him.
[US]‘O. Henry’ ‘Memoirs of a Yellow Dog’ in Four Million (1915) 111: Old Mother Hubbard was boosting me to beat the band.
[US]E. Pound letter Aug. in Paige (1971) 121: Ah, that one might live to see the expression on the face of a new poet, whom I had just been boosting, upon seeing another still newer poet seated in an armchair.
[UK]Wodehouse Inimitable Jeeves 15: Young Bingo must have boosted me to some purpose.
[US]W.M. Raine Cool Customer 19: Garside was a booster for his city. He began to promote the town at once.
[US]O. Strange Sudden Takes the Trail 152: I ain’t boostin’ it on that account.
[US]Lait & Mortimer USA Confidential 72: [He] is a hot booster of unions.
[US]Murtagh & Harris Cast the First Stone 12: Chances are, if a call-girl is easy to meet she is not, as her boosters boast, ‘top-drawer stuff.’.
[US]Wentworth & Flexner DAS.
[US]G. Liddy Will 75: I glanced up and stared at something that was, to me, remarkable: an outdoor advertising sign in which the persons shown happily boosting the product were black.
[US]Christian Science Monitor 31 Dec. 13: But a chorus of boosters [...] say the area will retain a lot of its unique character.
[US](con. 1964–8) J. Ellroy Cold Six Thousand 154: Clip Curtis and Leroy. Appease the Boys and play civic booster.

2. attrib. use of sense 1.

[US]S. Ford Shorty McCabe 178: No, I ain’t goin’ into the boostin’ line as a reg’lar thing.

In phrases

give the boost (v.)

(US) to praise a third party, esp. in context of preparing a victim for a confidence trick.

[US]F. Hutchison Philosophy of Johnny the Gent 9: The Wise Cracker thinks it’s the boost that had been shot in, an’ he says: ‘Why, certainly. I’ve been connected with this gent in the race hoss biz for several years’.