The couple, who have two sons aged five and six, were pronounced dead at the scene of the stabbing on Sunday evening.
Reeves, a former soldier in the 24 Commando Royal Engineers, appeared at Taunton magistrates court on Wednesday for a two-minute court hearing.
Wearing a grey prison-issue tracksuit, he spoke only to confirm his name and address and was remanded back into custody.
“Due to the nature of these offences this court has no power to deal with anything to do with it, and we have no power to deal with any bail matters”, said magistrate Stephen Howells.
Reeves, who also lives in Dragon Rise, is due to appear at Exeter crown court on Friday for a fuller hearing, including on the issue of bail.
Emergency services were called to the Chapple’s home at around 9.45pm on Sunday. Mr Chapple, 36, who worked at West Somerset College, and his 33-year-old wife, a staff member at a local garden centre, both died from multiple stab wounds.
Nine members of Reeves’ family were present in court for the brief court hearing. He stood motionless as the two murder charges were read to him.
One of his relatives was heard to call out “love you bro” and another told him to “stay strong” as Reeves was led from the dock.
A second man, aged 67, was also arrested on suspicion of the two murders on Sunday evening, and was released under investigation on Tuesday.
Chapple did not entered any pleas to the two counts of murder during his court appearance.