Boost

to lift or raise by pushing from behind or below.
to advance or aid by speaking well of; promote:
She always boosts her hometown.
to increase; raise:
to boost prices; to boost the horsepower of the car by 20 percent.
Slang. to steal, especially to shoplift:
Two typewriters were boosted from the office last night.
Slang. to engage in stealing, especially shoplifting.
an upward shove or raise; lift.
an increase; rise:
There’s been a tremendous boost in food prices.
an act, remark, or the like, that helps one’s progress, morale, efforts, etc.:
His pep talk was the boost our team needed.
Contemporary Examples

Could Bankruptcy Rescue the Twinkie? Megan McArdle November 19, 2012
TV’s Best and Worst Teachers Jaimie Etkin September 3, 2011
Speed Read: Eight Shocking Bits From the USADA’s Lance Armstrong Report Laura Colarusso, Nina Strochlic October 10, 2012
David’s Book Club: What Are Liberals Thinking? David Frum July 12, 2012
Hey, Yahoo, It’s Time to Grow Up Larry Kramer October 20, 2008

Historical Examples

The Man in the Twilight Ridgwell Cullum
Teddy: Her Book Anna Chapin Ray
The Corner House Girls on a Tour Grace Brooks Hill
Crooked Trails and Straight William MacLeod Raine
Old Crow Alice Brown

noun
encouragement, improvement, or help: a boost to morale
an upward thrust or push: he gave him a boost over the wall
an increase or rise: a boost in salary
a publicity campaign; promotion
the amount by which the induction pressure of a supercharged internal-combustion engine exceeds that of the ambient pressure
verb (transitive)
to encourage, assist, or improve: to boost morale
to lift by giving a push from below or behind
to increase or raise: to boost the voltage in an electrical circuit
to cause to rise; increase: to boost sales
to advertise on a big scale
to increase the induction pressure of (an internal-combustion engine) above that of the ambient pressure; supercharge
v.
boost
(bst)
A linear map from one reference frame to another in which each coordinate is increased or decreased by an independent constant or linear function. A boost corresponds to a shift of the entire coordinate system without any rotation of its axes.

To steal, esp by shoplifting: Someone had boosted my tape recorder out of the room/ slept on park benches and boosted from the A&P (1908+)
To praise highly: to boost one’s home town (1900+)
To do the sex act with or to; bonk, screw (1980s+ Students)