ES7 - how can I replace Promise with await?

One thing puts me off with Promise is that it is difficult to grasp with resolve and reject. Also the need of wrapping for Promise is ugly. Unless you use it very often, I tend to forget how to use them over time. Besides, code with Promise is still messy and hard to read. Hence I don't really like using it at all - because it has not much different from the callback hell. So I thought with ES7 await, I can avoid using Promise and giving me some more faith in JavaScript, but it seems that it is not the case. For instance:

const getOne = async () => {
    return Weather.findOne(options, function(err, weather) {
        //
    });
}
const getWeather = async () => {
    const exist = await getOne();
    if (exist == null) {
        return new Promise(function(resolve, reject) {
            // Use request library.
           request(pullUrl, function (error, response, body) {
                if (!error && response.statusCode == 200) {
                    // Resolve with the data.
                    resolve(body);
                } else {
                    // Reject with the error.
                    reject(error);
                }
            });
        });
    }
}

const insertWeather = async () => {
    try {
        const data = await getWeather();
    } catch (err) {
        res.set('Content-Type', 'application/json');
        return res.status(200).send('Error occurs: ' + err);
    }
}
insertWeather();

request(pullUrl, function (error, response, body) {} is an AJAX call from request package for nodejs.

I have to wrap it with Promise - but not precede it with await. Ideally this is what I imagine:

return await request(pullUrl, function (error, response, body) {...}

But if I do that, I will get the request object in return, instead of the data return from the request package - at this line:

const data = await getWeather();

Any ideas or solutions to avoid using Promise in the case such as the one above?