6x6 or 8x8. If you can find a big piece of cardboard, you can cut it to width and nail it to the existing post to give you an idea of scale.

Painted white, for example, will make them stand out as well.

You can have "skirts" built at their base to about 3 ft. up.

No to "skirts" on those posts. They're simply structural,and skimpy looking, probably 4x4 posts. Most places, they'd have been replaced (or dressed) with some kind of column, before you bought the home. Now, you will now have to do it.

There are a number of "kits' available to allow you to make them look bigger, if the post supports the load.

Four by four is standard. They look fine to me but if you want larger go up to six by six. My porch roof rests on a beam. Then the posts attache under the beam. I think it is a better look.

Double them up with another 4x4. You can leave a gap for a slightly arts and crafts appearance or slam them together and face them with facia boards. I would opt for the gap, adds detail.

Look for column wraps:

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6" Columns would look much better.