Can I put a 60 amp breaker in my sub panel that also runs ona 60 amp breaker from main panel
Depends on your feeder cable
The cable from the main panel to the subpanel is feeder.
The cable from the subpanel to the EVSE is a branch circuit.
A cable can't be both a feeder and a branch circuit. That is to say, the 60A feeder can't simply be tapped and also sent to the EVSE.   It needs to go to the subpanel, and then through a 60A branch circuit breaker.
Here's the thing.  There's no such thing as a 60A feeder. Does not exist.   Either

your wiring is 55A (#6 copper NM-B or UF-B or other #6 copper rated 60C temperature) and since 55A breakers don't exist, you round up to 60A breaker.  Or
your wiring is 65A (#6Cu or #4Al of a more advanced insulation type) and you downbreakered to 60A for some reason.

The difference is that in one case, you have 55A feeder. In the other case you have 65A feeder.  You cannot provision more load on the panel than the feeder can provide which may mean 55A.
With EVSEs, you must provision 125% of the actual ampacity.  So a 48A EVSE needs 60A provisioned to it (which is not the same as a 60A breaker).   You cannot provision 60A from a 55A feeder.
Room for everything else
We can take for granted that the welder and EVSE won't be in use at the same time; #1 they need to be in the same physical space, and #2 the supply breaker will say &quot;no way Jose&quot;.
However, we need to leave room for the two 20A circuits, and that's an imbroglio.  Code does not say &quot;just add up all the breaker trips&quot;.
First, the NEC 2014 requirement for a 20A circuit isn't a factor, because the purpose of that requirement is to power an EVSE and you are already providing that via separate means.  So that's off the table.
(and even if you had a second EV, Tesla's Wall Connectors know how to share, and Tesla uses the same protocol as the standard J1772 connector, so it will still work with a third party EV using an adapter).
The only other guidance NEC gives us for domiciles is a square-foot calculation of 3 VA per square foot (or 1 amp per 40 square feet) in NEC 220.12. 220.14(J) tells us not to worry about it for domiciles, since it's folded into the above 220.12 calculation... it says &quot;No additional load calculations shall be required for such outlets&quot;.  But that's intended as a catch-all for service to the entire domicile, it was never imagined for a garage subpanel.
The last guidance we have is for non-domiciles at 220.14(H) and (I)...  where 180 VA (1.5A) per receptacle is allocated.  A common duplex recep counts as 1.  A long surface conduit power strip counts as 1.  You need to do this for each of the 2 circuits, but since they are on opposite poles, you only need to count the larger.  Not a perfect solution, but Code does not cover this well.
By my math, 3 receptacles = 4.5A + the 60A provisioned to the EVSE = 64.5A.
That's OK on a 65A feeder. Though you might want to address the under-breakering of that feeder e.g. by fitting a 70A breaker.
If it's a 55A feeder, you'll need to set the DIP switches inside the EVSE to advertise itself as a 40A unit (understand how EVSE ampacity works).  That way, the EVSE derates 125% to 50A.  That + e.g. 4.5A for the receps = 54.5 amps and you're in limits.