Is it safe to connect to a Weak Security WiFi on my iPhone?

No, it is not safe.

Check your WiFi Router / Modem for --> Recommended settings for Wi-Fi routers and access points ...

Consider more secure wifi configuration.

Change your router’s WiFi to use WPA2-AES (CCMP) with no WPA or TKIP. Updating this setting ensures that your devices always connect in one encryption mode

1. TKIP is obsolete and not considered secure. Choose WPA2, the latest encryption standard, with AES encryption for optimal security
2. If your router doesn’t specify TKIP or AES, the WPA2 option probably uses AES

See the pics below

I advise against it. Cyberspace has a lot going on right now and it could potentially put your device at risk.