The excerpt that best implies Tweedledee is a silly character is:
"All this time Tweedledee was trying his best to fold up the umbrella, with himself in it: which was such an extraordinary thing to do, that it quite took off Alice's attention from the angry brother."
This line indicates Tweedledee's nonsensical and silly behavior, as trying to fold up an umbrella with himself inside it is a ridiculous and impractical task, highlighting his silliness.