How do I benchmark latency with different packet sizes?

I’m trying to benchmark network latency with different packet sizes. Standard ICMP ping works great until a payload size of 1 KB. After that, it becomes increasingly unreliable with packet drop rates of > 80%. I also tried Ultra Ping which sends pings over UDP but none of the echoes reflected by the server arrive at the client.

When tunneling traffic via VPN everything works fine.