Pass in parameters instead of multiple functions
I'd put the cookies into an object so they can be named.

var userCookies = {
    height: {
        name: 'user-height',
        options: {
            path: '/',
            expires: 365
        }
    },
    weight: {
        name: 'user-weight',
        options: {
            path: '/',
            expires: 365
        }
    }
};


Then you only need read/write cookie methods: (I've not used $.cookie so I'm only guessing I haven't broken it.)

function readCookie(cookieName) {
    var userData = $.parseJSON($.cookie(userCookies[cookieName].name));
    return(userData);
};

function writeCookie(userInfo, cookieName) {
    $.cookie(weight_cookie.name, JSON.stringify(userInfo),userCookies[cookieName].options);
};


If you want to be really modular (like all the cool kids) you might do something like:

var CookieMonster =(function ($) {
    var userCookies = {
        height: {
            name: 'user-height',
            options: {
                path: '/',
                expires: 365
            }
        },
        weight: {
            name: 'user-weight',
            options: {
                path: '/',
                expires: 365
            }
        }
    };
    return {
        readCookie: function readCookie(cookieName) {
            var userData = $.parseJSON($.cookie(userCookies[cookieName].name));
            return(userData);
        },
        writeCookie: function writeCookie(userInfo, cookieName) {
            $.cookie(weight_cookie.name, JSON.stringify(userInfo),userCookies[cookieName].options);
        }
    };
})(jQuery);

var userInfo = CookieMonster.readCookie('height');
var userInfo2 = CookieMonster.readCookie('weight');