Well, for one, your links are being activated and reloading the page.
Typically when you write jQuery, you would attached the events using selectors, not using inline code. This let's you keep your JavaScript and HTML in separate files as well as allows jQuery to remove events when needed.
<a href="#" id="bigText">big text</a>
$('#bigText').click( function(event) {
// code here
} );
Then to prevent the default action (following the link), you can use the jQuery method, prevent default action.
$('#bigText').click( function(event) {
event.preventDefaultAction();
// code here
} );
You may also what to wrap you event binding code withing a document ready event in order to make sure that the DOM is loaded before trying to attach events to it.
$(document).ready( function() {
$('#bigText').click( function(event) {
event.preventDefaultAction();
// code here
} );
} );
Also, you would typically want to add a class to change an element's styles rather than using jQuery to change the style. It's more performant. Also, if you want to only affect element within a container, you can use the jQuery "find" method to do so.
$('#someContainer').find('p').addClass('someClass');