Latest Public Health Scotland figures for 14 May show the local authority rate is up at 46 per 100,000. Just two days earlier, on May 12, the rate was 31.
Cases had gone down from the beginning of the month when the seven-day infection rate per 100,000 population stood at 48.8.
Now, just a day after the area moved up into level two, cases are spiking again. The threshold for level two is 50 cases per 100,000,
In neighbouring Glasgow, the number of Covid infections is continuing to rise, with weekly case rates now higher than 100 per 100,000 people. There are now four council areas in Scotland with case rates higher than 50.
Two of them - Glasgow and Moray - have been held at level three restrictions. Moray's rate for the 14 May was 55.2, but that now appears to be falling.
Midlothian has a rate of 55.2, with indications it is rising.
Scotland's national clinical director, Prof Jason Leitch told BBC Scotland other areas would continue to be monitored. He said people were being asked to get tested and vaccinations were being rolled out as fast as possible.
"I'm hopeful that we won't have to go backwards but I can't guarantee it," he said.
"It can't be as simple as case rates. Everything builds from there, from hospitalisations, intensive care admissions and death, tragically.
"But you've also got to think about things like vaccine coverage, the economy and social harm. Today we are allowing people into each other's houses - that's a fantastic step but not so good for the public health advisers. You have to balance all that."
Prof Leitch said not enough was yet known about the impact of the Indian variant, but added that in the north of England it had not led to an increase in hospital admissions and numbers of people in intensive care.
He urged anyone in an area with increasing cases to get tested and said people should be doing home tests twice a week as an "extra layer of protection".
He added that people should remain cautious but should not panic.