This time of the year you can see high humidity inside the hive, to the point of condensation, depending on hive type (materials like dense polystyrene or acrylics breathe less and so build up more moisture inside).
Hypothesis: the observed weight increase is due to condensation, and the seemingly correlated (but slightly delayed) increase in temperature seen is due to the fanning activity of the colony in response.
Other variables of interest would be sound (is there ventilation activity evident in the FFT?) and outside temperature (expect to see an inverse relationship between in-hive humidity and outside temperature). You can consider hooking up a relative humidity sensor such as a BME280; simply connect it to the the same I2C-bus as the temperature sensor, as described in the helpdesk article on connecting additional temperature sensors.
I believe this is due to temperature drift of the load cell used to measure the hive weight. With typical scales, a tare is made each time the scale is used. With an hive scale it is impossible whereas it would be needed because there are multiple physical reasons for the load cell output to vary with temperature. It is possible to incorporate a temperature compensation algorithm to minimise the load cell temperature drift but it's hard to totally eliminate it. Also the drift is highly depending on the load cell (of the same model). Beep base is using an H40 load cell from Bosche and I have measured temperature drift from 1g/°C to 7g/°C.
During the year I noticed that on 1 of my beep bases the weight seems to follow the outside temperature. The other base doesn't do that, but it has another problem.
What could be the problem?