If the earth's radius was half as large as it currently is but with the same mass, how would the acceleration of gravity at the earth's surface change, and by how much

The acceleration of gravity depends on two things.

One thing is the planet's mass, so that wouldn't cause it to change.

The other thing is the square of your distance from the planet's center.
You said that the distance is reduced to 1/2 of what it used to be, so
that tells us that the acceleration of gravity ... and the weight of every
thing and everybody on Earth ... would increase by 2² = 4 times.

Answerthe global climate during the paleogene departed from the hot and humid conditions of the late mesozoic era and began a cooling and drying trend which dispite having been periodically disrupted by warm periods such as the paleocene-eocene thermal maximum, persists today;