You've mentioned you can actuate the latch with your finger - I assume that means the latch itself is working reasonable well, which to me would still point to an issue with alignment or binding on the post.
Does the door move smoothly as it engages the post/striker? If you close it slowly, can you see the door shift up or down while it's latching closed? Does it sound smooth, or is there any sound of excessive rubbing?
If you have the weatherstrip, and you're at that point anyway, I'd install it and see if that makes any difference at all.
