Colby was commissioned lieutenant on 11 March 1742 and promoted commander on 30 March 1746 when he joined the newly purchased Albany 14 at Louisbourg. He held the command of this vessel for a few months only until she was captured by the French frigate Castor 28 in Chedabucto Bay, Nova Scotia on 19 July 1746 with the loss of one man killed.
Following the end of the War of Austrian Succession in 1748 he commanded the Grampus 10 out of Greenock, Scotland, returning to Plymouth at the end of the latter year and then going around to the Nore in 1752.
Colby was posted captain of the newly launched Deal Castle 24 on 20 August 1756 although he did not take her to sea, and in July of the following year he was appointed to the Princess Amelia 80, joining Admiral Sir Edward Hawke?s expedition to Rochefort with the flag of Rear-Admiral Thomas Broderick. In April 1758 he commissioned the new Thames 32 for service in the Channel, but later in the year lost an eye after being hit by a musket ball in an action off Brest, for which impairment he was granted a 150 guinea pension.
Continuing in the Thames, he earned a great deal of acclaim when in company with the Coventry 28, Captain Carr Scrope, he fought an action with the French sail of the line Palmier 74 in March 1759. Initial contact was made off the Scilly Islands on the morning of the 12th, and in rough weather that prevented the Frenchman from opening its lower gun-ports the Thames chased her larger opponent and an accompanying frigate towards Brest, occasionally heaving too and exchanging broadsides. At one point the Thames was obliged to break off the action with five feet of water in her hold and the magazine floor flooded, but when the Palmier resumed her course towards Brest Colby brought the Thames with the Coventry under her stern on the darkening afternoon of the 13th and raked her for several hours until she entered port.
On 18 May 1759 he earned further honour when he assisted the Chatham 50, Captain John Lockhart, and Venus 36, Captain Thomas Harrison, in the capture of the French frigate Arethusa 32 in Audierne Bay, being instrumental in forcing her into action and losing four men killed and eleven wounded. He remained in the Thames for another year, capturing the Morech 18 in company with the Coventry off Le Havre, and taking the privateer Bien Aime 36 off Tory Island on 26 September.
In January 1771 he recommissioned the guardship Kent 74 at Plymouth, retaining her but a year.
Colby was not employed thereafter until September 1777 when he joined the recommissioned Fame 74. He commanded her in Vice-Admiral Hon John Byron?s fleet that was sent out to North America on 9 June 1778, arriving off New York on 28 August after a storm has driven the ships apart. He later departed for the Leeward Islands in December with Byron but the Fame was dismasted within four days of sailing and was kept in company by the Diamond 32, Captain John Linzee, for another week before a further gale parted them near the Bermudas. Eventually the Fame made it into Barbados under a jury rig.
Captain Colby continued to command the Fame in the Leeward Islands during the early part of 1779 but he died later that year.
He bought the elegant property of Ffynnonau in Pembrokeshire in 1752, the ownership of which passed to his nephew on his death.