Question: I came across with this video in which the Falcon Heavy boosters' landing burn seems to deaccelerate the 1st stage until a point their speed is constant right before touchdown.

Can the 1st stage maintain a constant speed, and eventually hover? Did they tweaked the 1D enough to throttle deeper than before?

Answer: 
The falcon 9 first stage **cannot** hover as the thrust of one Merlin engine even at its lowest thrust is able to overcome the mass of the almost-empty first stage. The stage appears to decelerate very slowly in the final moments of the landing as a result of the engine firing pattern SpaceX uses.

Per Elon Musk:

> 
> Thanks! 3 of 9 engines are lit initially, dropping to 1 near ground. Even w 1 lit, it can't hover, so always land at high g
>  - Elon Musk (@elonmusk) April 15, 2015
> 
> 
> 

So as soon as the 3 engines are fired, the stage decelerates rapidly, but when the two outer ring engines are shut down for final approach, the deceleration of the stage slows rapidly, giving the illusion that it is hovering. Although this tweet is from early 2015, we know that the engines on the Falcon 9 have only gotten stronger, so it would have no chance of hovering. In order to land, SpaceX uses a hover-slam or suicide burn, so as soon as the stage reaches zero velocity while decelerating, it’s on the ground/ASDS. Blue Origin’s [New Shepard](https://en.m.wikipedia.org/wiki/New_Shepard) rocket, however, can hover above the ground and does so to travel laterally before landing on the pad.
The Merlin 1D claims to be able to throttle to 40%, which would be about 350 kN thrust at sea level. The dry mass of a Falcon 9 first stage is about 24 tons, so it can't hover, but it can get pretty close. Thrust to weight would be about 1.3.
All data from wikipedia.