The server is sending your certificate, but it also needs to send the Let’s Encrypt Authority X3 intermediate certificate. Web browsers will sometimes compensate; wget doesn’t.
https://www.ssllabs.com/ssltest/analyze.html?d=blackdog.straight8.com&hideResults=on
Since you’re using Apache 2.4.6, you have to add an SSLCertificateChainFile directive pointing to a file containing the intermediate certificate(s).
For example, if you’re using Certbot, it’s the chain.pem file, so you’d set something like “SSLCertificateChainFile /etc/letsencrypt/live/example.com/chain.pem”.