Where to connect thermostat C wire to Weil-McLain HE2 series 1 boiler
Both this document (PDF) and this document (PDF), say that one 24V-40VA transformer can only support 3 zone valves. Since you have 4 valves, you're over the recommended number of valves.  Once you added the demand of the WiFi thermostat, you likely overwhelmed the transformer. The answer here, may be to install an additional transformer. 

There's a diagram in the second document, that shows how to wire in an additional transformer. This document also has a good explanation of how the valve actually works, which might be worth a read. 


  


Based on these documents, a WiFi thermostat should be wired in like this.



Based on the your description of the wiring, it sounds like it's a bit different than that of the documentation. Incorrectly wired valves might also be the problem. Based on the documentation, terminals 1 and 2 are connected through a heater, while terminals 2 and 3 are connected only when the valve is open.

When the thermostat closes (calls for heat), current flows from terminal 1, through the heater, to terminal 2. Once the valve opens, a contact allows current to flow between terminals 2 and 3.  So basically energizing 1 and 2 opens the valve, and energizing 2 and 3 signals the boiler to circulate.