sip at

sip at (something)

To take small sips of a drink over a period of time. My favorite thing to do is watch the sun come up while I sip at my first coffee of the day. It always makes me self-conscious when someone I'm out with sips at one or two drink throughout the whole evening while I'm getting a fresh pint every half hour.
See also: sip
Farlex Dictionary of Idioms.

sip at

or sip on
v.
To drink from some beverage in small amounts at a time: The skier sipped at the hot coffee at the lodge. She was sipping on a cocktail at the bar.
See also: sip
The American Heritage® Dictionary of Phrasal Verbs.
See also:
  • sip
  • sip at (something)
  • sip on (something)
  • do the drink thing
  • be in the drink
  • name your poison
  • pick your poison
  • What are you drinking?
  • What are you having?
  • What would you like to drink?
References in classic literature
There was an attractive spot among the trees where were a great many wooden tables and benches; and there one could sit in the shade and pretend to sip at his foamy beaker of beer while he inspected the crowd.
Tramp Abroad