Both Mr. Enfield and Mr. Utterson suspect that Mr. Hyde is blackmailing Dr. Jekyll with some information, perhaps about the doctor's behavior when he was young, or "some of the capers of his youth."  Mr. Enfield says, after seeing Mr. Hyde, that it simply isn't possible that anyone would be friends with him of their own accord.  However, the fact that Mr. Hyde had produced, in Mr. Enfield's story, a check signed by Dr. Jekyll, a check that was obviously not forged, leads Mr. Enfield to refer to the house into which Mr. Hyde went to retrieve this check the "Black Mail House."  The fact, also, that Mr. Hyde has a key to this house is further indication of some intimate relationship between the two men, and Mr. Hyde's "'damnable'" character makes it impossible that he could be friends with someone like Dr. Jekyll, who "'is the very pink of proprieties."

After their walk together in Chapter 1, both Enfield and Utterson suspect that there is something wrong about the relationship between Jekyll and Hyde.  They both seem to think that there is some sort of coercion going on.

Enfield believes that Hyde must be blackmailing Jekyll and that is why Jekyll gave Hyde the check to compensate the family of the girl he trampled.

Utterson knows that Jekyll's will specifies that Hyde should take over his possessions if Jekyll should go missing.  Because of this Utterson is afraid that Hyde is somehow controlling Jekyll.

So, at this point, neither suspects that Jekyll and Hyde are alter egos, but they worry about Hyde controlling Jekyll.