DIAGNOSIS You're right, the float valve up just means the lid is sealed. The weight not rocking means internal pressure hasn't reached the level needed to lift it. The most common cause is the heat source isn't strong enough for a pot this large, especially on an electric stovetop.
FIX 1) After the float valve seals, you need to turn the heat up higher to bring it to pressure faster. On a gas stove, a medium-high flame under a 13-quart pot is typical. On electric, you might need to start on high. 2) Once you see a steady stream of steam from the open vent (with the weight off), let it vent for a full minute to purge air from the system. 3) Then place the correct weight for your pressure setting (e.g., 15 psi for canning) on the vent pipe. It should start rocking rhythmically within a few minutes.
IF THAT DIDN'T WORK Check that you're using the right weight. Some cookers have multiple weights for different PSI settings. Using a 5 psi weight on a canning recipe that needs 15 psi will mean it never rocks at the expected heat level.
HEADS UP Timing for the recipe only starts once the weight begins its steady, rocking rhythm. The time between the float valve sealing and the weight rocking is just ‘come-up’ time and doesn't count toward cook time.