Yes, some sites do, but in most cases this is actually a psychological effect. As prices tend to go up the closer to departure date you get, it’s natural that it looks like the site is raising them between visits.
Long before the departure date this effect may not be significant, but a large portion of all bookings, in particular on short distance flights, is happening within 14 days of departure. That’s also the time period in which the price, on many routes, increases exponentially.
Average lowest price from Stockholm to Berlin
Still there are sites that run this cookie schema, and it’s mainly seen on airline sites. It’s based on the knowledge that users often looking their flights up in advance of coming back to book it.
So when you are coming back, they raise the price with a certain amount (€10, £10, 100kr, etc.) as they know you are interested in this particular route and likely to book it anyway.
So how can you avoid being fooled into paying this extra fee?
The best way to dodge this trick is to stick to price comparison sites - such as Avionero, Skyscanner, Flygstolar, Aviasales or any other - all the way until you are ready to actually book your ticket.
Since price comparison sites are not performing any actual bookings, they are unable to run this schema, but must rely entirely on the prices they receive from their contracted booking sites.
These contracted booking sites, on the their side, are unable to run this schema against you as they don’t have access to the tracking information stored on the price comparison site.
So in summary:
Keep your cookies, they are safe and they help you get better search results, and then stay on Avionero until you are ready to go ahead and book your ticket. In that way you both get the best flights and be safe from these unfair cookie (or other tracking-based) markup schemas.