Chrome Extension: Make it run every page load

From a background script you can listen to the chrome.tabs.onUpdated event and check the property changeInfo.status on the callback. It can be loading or complete. If it is complete, do the action.

Example:

chrome.tabs.onUpdated.addListener( function (tabId, changeInfo, tab) {
  if (changeInfo.status == 'complete') {

    // do your things

  }
})

Because this will probably trigger on every tab completion, you can also check if the tab is active on its homonymous attribute, like this:

chrome.tabs.onUpdated.addListener( function (tabId, changeInfo, tab) {
  if (changeInfo.status == 'complete' && tab.active) {

    // do your things

  }
})

If it needs to run on the onload event of the page, meaning that the document and all its assets have loaded, this needs to be in a content script embedded in each page for which you wish to track onload.