The primary hardening mechanism for aluminum alloys is the precipitation of secondary phase particles in the matrix. This contrasts most steels where hardening is primarily achieved through solute addition to the matrix and precipitation of secondary phases at grain boundaries.
The hardening process in aluminum alloys therefore requires a more extensive heat treatment process, and makes them more prone to thermal shock. In weldability terms, this means that some aluminum alloys, when welded, are extremely likely to crack on cooling. This can also be the result of different rates of thermal expansion between the aluminum matrix and the secondary phase. To the best of my knowledge, 7075 is on the list of aluminum alloys that are not considered weldable, along with most cast Al alloys.
Can 6061 be welded to 7075? Probably, with enough patience, something will stick. It's highly inadvisable to make any sort of structural weld with these two alloys due to the risk of cracking.
What equipment do you have at your disposal? Al welding also requires a way to deal with the almost instantaneous formation of oxides on the Al surface: typically, a TIG setup with AC, or occasionally, special sticks with a reducing flux (I have a box of these but have never used them and understand they have probably been discontinued for some time due to the difficulty of use).
You might have better success brazing two aluminum pieces together; while the filler rod is typically much more expensive, the likelihood of making a viable joint is much higher given appropriately selected filler.