*seku̯-

The original sense of the root was:

following, pursuing

If we think of this in a context of hunting, we can easily see why how this root evolved into the words to see (from following with eyes) and to say (telling what you see). The connection of “to say” is debated, though.

The original sense of following is well preserved in the Latin branch around  *sequi (to follow) with words like sequence, sect or execute.

Also the words around social likely belong to this family.
Here’s an (incomplete) list of the relatives in English:

• social, associate, society… (“followers, going together”)
• sequence, sequel, second, sect, segue (“what follows”)
• pursue, persecute, prosecute (“going/come after”, basically prefix versions of the Latin base verb)
• execute (to follow through)
• to see (“follow with eyes”)
• to say (“tell what you see”)