I love Bookmarklets, they let you quickly customise web sites in a lighter way than a Chrome extension, and for the longest time (5 years), I thought it wasn't possible to run Bookmarklets on Chrome on Android.
It turns out, I was wrong. You just can't run them the traditional way.
The way that most people access Bookmarks on Android doesn't let you run a Bookmarklet, i.e, via "Select Bookmarks" in the main menu;

And then then picking their bookmark from the list of bookmarks

This is because Chrome on Android seems to have no knowledge of the current page the user is on, and therefore can't execute JavaScript against that page.
I was today years old when I learnt that you can find bookmarks via the Address Bar, and they keep the context of the current page. This means that you can run Bookmarklets.
Here is the exact trick to make it work:
- Tap into the Address Bar while on the page where you want to run the bookmarklet.
- Start typing the exact name of your bookmark (give it an easy, distinctive name so it doesn't get buried under search suggestions).
- Look at the autocomplete suggestions below the address bar. Don't press Enter or tap a search suggestion — look specifically for the suggestion with the star / bookmark icon matching your bookmark title.
- Tap that bookmark suggestion. Chrome executes the bookmarklet in the context of the currently active page.

(Note: You might wonder why you can't just paste the javascript:... code directly into the address bar and hit Go. Chrome automatically strips the leading javascript: scheme on paste for security reasons, so invoking the bookmark via address bar autocomplete is the only reliable method).
Voila.
Now that I know you can use bookmarklets via the address bar, this opens up a lot of options for slightly deeper customisation on Android than what is possible today.