Unequal randomization by a certain factor

I think the simplest way with the built-in features is to use Quotas and randomization of the responses you want. In your Survey Flow, add a randomizer with eight embedded data elements (Group1, Group1, Group1, Group1, Group1, Group2, Group2 Group2). This weights your randomization for each person to 62.5% (Group1) and 37.5% (Group2). Then use branching logic to check which group element was selected and display your questions for that condition. If the quota for that condition is full, then reassign them to the other condition so you don't burn sample because the program won't check the weighting as you field to make sure answers are falling out exactly this way. You use quotas to control back to the exact number of responses you want in each condition.
Assign to group
Show condition
Tally your quotas (not I've simplified down to smallest number to keep your ratio)
Set quotas to stop collection

• Total = If Intro is displayed, When met then End Current Survey


• Total (Fake Close) = If Intro is displayed, When met then Prevent all new survey sessions

Survey file attached. I ran his twice and filled it in as follows:

Time 1: Group1, Group2, Group2, Group1, Group1, Group2, Group2 (but showed Group1), Group1
Time 2: Group2, Group2, Group1, Group1, Group2, Group2 (but showed Group1), Group2 (but showed Group1), Group1
Weighted_Randomization.qsf