Build packages as wheels, then install in small container.

Dockerfile

FROM python:3.7-slim-stretch AS build

RUN \
  apt-get -q update \
  && apt-get -q install -y --no-install-recommends \
    build-essential \
    libssl-dev \
  && rm -rf /var/lib/apt/lists/* \
  && pip install -U pip

WORKDIR /build

ADD constraints.txt /build/constraints.txt

ENV \
  PIP_WHEEL_DIR=/build/wheelhouse \
  PIP_NO_CACHE=true \
  PIP_CONSTRAINTS=/build/constraints.txt

RUN pip wheel -r constraints.txt --no-cache-dir

FROM python:3.7-slim-stretch

RUN \
  apt-get -q update \
  && apt-get -q upgrade -y \
  && apt-get -q install -y --no-install-recommends \
    libssl1.1 \
  && rm -rf /var/lib/apt/lists/* \
  && pip install -U pip

COPY --from=build /build/wheelhouse /tmp/wheelhouse

WORKDIR /app

ADD setup.py /app/

ENV \
  PIP_FIND_LINKS=/tmp/wheelhouse \
  PIP_NO_INDEX=true \
  PIP_NO_CACHE=true

RUN pip install -e .

ADD gunicorn.conf.py /app/
ADD src /app/src

RUN useradd app
USER app

EXPOSE 8080

ENTRYPOINT ["/usr/local/bin/gunicorn", "-b", ":8080", "-c", "gunicorn.conf.py", "app:load_wsgi_app()" ]